Adaptive MA constructor [lastguru]Adaptive Moving Averages are nothing new, however most of them use EMA as their MA of choice once the preferred smoothing length is determined. I have decided to make an experiment and separate length generation from smoothing, offering multiple alternatives to be combined. Some of the combinations are widely known, some are not. This indicator is based on my previously published public libraries and also serve as a usage demonstration for them. I will try to expand the collection (suggestions are welcome), however it is not meant as an encyclopaedic resource, so you are encouraged to experiment yourself: by looking on the source code of this indicator, I am sure you will see how trivial it is to use the provided libraries and expand them with your own ideas and combinations. I give no recommendation on what settings to use, but if you find some useful setting, combination or application ideas (or bugs in my code), I would be happy to read about them in the comments section.
The indicator works in three stages: Prefiltering, Length Adaptation and Moving Averages.
Prefiltering is a fast smoothing to get rid of high-frequency (2, 3 or 4 bar) noise.
Adaptation algorithms are roughly subdivided in two categories: classic Length Adaptations and Cycle Estimators (they are also implemented in separate libraries), all are selected in Adaptation dropdown. Length Adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle Estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement or the rate of change (the rate of change may also differ depending on the cycle phase, but the cycle period itself usually changes slowly).
Chande (Price) - based on Chande's Dynamic Momentum Index (CDMI or DYMOI), which is dynamic RSI with this length
Chande (Volume) - a variant of Chande's algorithm, where volume is used instead of price
VIDYA - based on VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
VIDYA-RS - based on Vitali Apirine's modification of VIDYA algorithm (he calls it Relative Strength Moving Average). The period oscillates from the Upper Bound down (fast)
Kaufman Efficiency Scaling - based on Efficiency Ratio calculation originally used in KAMA
Deviation Scaling - based on DSSS by John F. Ehlers
Median Average - based on Median Average Adaptive Filter by John F. Ehlers
Fractal Adaptation - based on FRAMA by John F. Ehlers
MESA MAMA Alpha - based on MESA Adaptive Moving Average by John F. Ehlers
MESA MAMA Cycle - based on MESA Adaptive Moving Average by John F. Ehlers, but unlike Alpha calculation, this adaptation estimates cycle period
Pearson Autocorrelation* - based on Pearson Autocorrelation Periodogram by John F. Ehlers
DFT Cycle* - based on Discrete Fourier Transform Spectrum estimator by John F. Ehlers
Phase Accumulation* - based on Dominant Cycle from Phase Accumulation by John F. Ehlers
Length Adaptation usually take two parameters: Bound From (lower bound) and To (upper bound). These are the limits for Adaptation values. Note that the Cycle Estimators marked with asterisks(*) are very computationally intensive, so the bounds should not be set much higher than 50, otherwise you may receive a timeout error (also, it does not seem to be a useful thing to do, but you may correct me if I'm wrong).
The Cycle Estimators marked with asterisks(*) also have 3 checkboxes: HP (Highpass Filter), SS (Super Smoother) and HW (Hann Window). These enable or disable their internal prefilters, which are recommended by their author - John F. Ehlers. I do not know, which combination works best, so you can experiment.
Chande's Adaptations also have 3 additional parameters: SD Length (lookback length of Standard deviation), Smooth (smoothing length of Standard deviation) and Power (exponent of the length adaptation - lower is smaller variation). These are internal tweaks for the calculation.
Length Adaptaton section offer you a choice of Moving Average algorithms. Most of the Adaptations are originally used with EMA, so this is a good starting point for exploration.
SMA - Simple Moving Average
RMA - Running Moving Average
EMA - Exponential Moving Average
HMA - Hull Moving Average
VWMA - Volume Weighted Moving Average
2-pole Super Smoother - 2-pole Super Smoother by John F. Ehlers
3-pole Super Smoother - 3-pole Super Smoother by John F. Ehlers
Filt11 -a variant of 2-pole Super Smoother with error averaging for zero-lag response by John F. Ehlers
Triangle Window - Triangle Window Filter by John F. Ehlers
Hamming Window - Hamming Window Filter by John F. Ehlers
Hann Window - Hann Window Filter by John F. Ehlers
Lowpass - removes cyclic components shorter than length (Price - Highpass)
DSSS - Derivation Scaled Super Smoother by John F. Ehlers
There are two Moving Averages that are drown on the chart, so length for both needs to be selected. If no Adaptation is selected ( None option), you can set Fast Length and Slow Length directly. If an Adaptation is selected, then Cycle multiplier can be selected for Fast and Slow MA.
More information on the algorithms is given in the code for the libraries used. I am also very grateful to other TradingView community members (they are also mentioned in the library code) without whom this script would not have been possible.
Komut dosyalarını "algo" için ara
Exotic SMA Explorations Treasure TroveThis is my "Exotic SMA Explorations Treasure Trove" intended for educational purposes, yet these functions will also have utility in special applications with other algorithms. Firstly, the Pine built-in sma() is exceedingly more efficient computationally on TV servers than these functions will be. I just wanted to make that very crystal clear. My notes elaborate on this in the code blatantly.
Anyhow, the simple moving average(SMA) is one of the most common averaging filters used in a wide variety of algorithms. "Simply put," it's name says a lot about it. The purpose of this script, is to demonstrate variations of it's calculation in a multitude of exotic forms. In certain scenarios our algorithms may require a specific mathemagical touch that is pertinent to our intended goals. Like screwdrivers, we often need different types depending on the objective we are trying to attain. The SMA also serves as the most basic of finite impulse response(FIR) algorithms. For example, things like weighted moving averages can be constructed by using the foundational code of SMA.
One other intended demonstration of this script, is running multiple functions for comparison. I have had to use this from time to time for my own comparisons of performance. Also, imbedded into this code is a method to generically and recklessly in this case, adapt an algorithm. I will warn you, RSI was NEVER intended to adapt an algorithm. It only serves as a crude method to display the versatility of these different algorithms, whether it be a benefit or hinderance concerning dynamic adaptability.
Lastly, this script shows the versatility of TV's NEW additions input(group=) and input(inline=) upgrades in action. The "Immense Power of Pine" is always evolving and will continue to do so, I assure you of that. We can now categorize our input()s without using the input(type=input.bool) hackTrick. Although, that still will have it's enduring versatility, at least for myself.
NOTICE: You have absolute freedom to use this source code any way you see fit within your new Pine projects. You don't have to ask for my permission to reuse these functions in your published scripts, simply because I have better things to do than answer requests for the reuse of these functions. Sufficient accreditation regarding this script and compliance with "TV's House Rules" regarding code reuse, is as easy as copying the functions in their entirety as is. Fair enough? Good!
When available time provides itself, I will consider your inquiries, thoughts, and concepts presented below in the comments section, should you have any questions or comments regarding this indicator. When my indicators achieve more prevalent use by TV members, I may implement more ideas when they present themselves as worthy additions. Have a profitable future everyone!
Indexrate Code SMIndexrate Code SM is an indicator and part of the Indexrate Code Set of Algorithm, which additionally includes the Indexrate Code A strategy and Indexrate Code B indicator.
The Indexrate Code Set of Algorithms can be used for any trading instruments and on any existing markets (Stock market, Forex, Cryptocurrency market, etc.).
Getting access to the Indexrate Code A strategy, you gain access to the whole set of Indexrate Code algorithms.
Indexrate Code SM is an indicator, based on the Smart Money concept. Smart money is large market participants with sufficient volumes to influence the price. This is a small group that includes banks and large funds. Their every move is controlled down to the smallest detail. In the modern world, this is done with the help of artificial intelligence and other complex algorithms that move the price to certain values. Unique programs that lower and raise the price are effective because they know the behavior of people, which will invariably be based on fear and greed.
On the other side are the majority of traders, including us - this is uninformed money. This group includes retail traders and small funds. Residents of this group believe that due to their numbers, they move the market. But in fact, the retail sector cannot have any influence on the price. This is due to low volumes: a large group in monetary terms is not as large as it may seem. Large volumes that can do this are in a small group - smart money. Retail traders are too small and make up only a small percentage of the money in circulation on the market (~5%), so the main target for smart capital is always funds.
Smart Money is following large market participants. With the help of this concept and its tools, you can identify and track the actions of smart money. As long as there is liquidity in the market, the concept will be effective in application.
Indexrate Code SM consists of a set of signals displayed on the chart, configured in a unique way to interact with each other and allowing traders to comprehensively analyze the movement of the asset price.
The indicator displays the zones of interest of "bulls" and bears", which are highlighted with lines of the corresponding color. Where gray is the zone of "bears", and blue is the zone of "bulls". When these zones are broken, the indicator displays the corresponding signals to buy or sell.
The indicator also displays the zone of fair price, highlighting it in yellow. This zone acts as a conditional magnet in the event of a price rebound from the zones of interest.
In addition, the indicator displays the zone of the greatest local interest of buyers (storng high) and sellers (weak low). When the zone of fair price is broken, the asset often rushes to these local levels. From which a rebound often occurs, both during a reversal of movement and during a breakout.
The lines of the previous daily high (PDH) and the previous daily low (PDL) give traders an understanding of the intraday range of price movement.
The Indexrate Code SM integrates the Sequential and Trend HMA trend algorithms, known to us from the Indexrate Code A strategy. By default, these algorithms are not displayed on the chart (you can enable the display in the settings), since they are displayed in the strategy, but they continue to work inside the indicator to establish more accurate signals to buy or sell. The settings of these algorithms are identical to the settings displayed in the Indexrate Code A strategy.
The search for optimal signal settings includes the time structure, that is, the period for which the calculation and search for areas of interest are carried out. As well as the number of order blocks.
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The settings of the Sequential and Trend HMA trend algorithms are aimed at eliminating false signals as much as possible.
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The signals on the chart are displayed as green dots for buying and red dots for selling.
Provided that the Indexrate Code A strategy is configured most successfully, the appearance of a confirmation signal can provide the potential probability of the strongest price movement.
It is also worth considering that when working with the Heiken Ashi chart, for which the Indexrate Code Set of Algorithm works, you must install OHLC as shown in the screenshot below. Since this parameter allows you to take into account real exchange prices, without calculating average Heiken Ashi values, which can mislead the trader regarding the current state of the market. And also take into account the percentage of the exchange commission and the On bar close parameter.
telegra.ph
The Indexrate Code Set of Algorithms is suitable for conservative traders who evaluate their success in the long term, and not in short-term excess profits.
IT IS IMPORTANT TO KNOW that no indicator is capable of 100% predicting a successful trade.
The market is a collection of people. It is thanks to human psychology that shapes the forces of supply and demand that financial markets exist (Charles Dow Theory).
Forecasting based on the analysis of mathematical algorithms (indicators) uses data from past trading - the price of the previous period of time and the volume of previous trading. It is these two indicators that are used by modern technical analysis.
The Indexrate Code Set of Algorithm is based on algorithms that evaluate trends, prices and volume indicators. As well as human psychology, which requires an assessment of the exact preceding periods for a specific timeframe, and not an assessment of the entire period from the moment of listing of a trading instrument on a specific exchange. Since market indicators completely change throughout the trading period and the exchange trading volume also changes.
All updates to the Indexrate Code Set of Algorithm will be free.
Trading is trading on probabilities. Investing is trading on opportunity. Nobody knows the future - Always protect your profits!
Russian translation
Indexrate Code SM - это индикатор являющийся частью Комплекта алгоритмов Indexrate Code, включающего в себя дополнительно стратегию Indexrate Code А и индикатор Indexrate Code B.
Комплект алгоритмов Indexrate Code, может быть использован для любых торговых инструментов и на любых существующих рынках (Фондовый рынок, Форекс, Криптовалютный рынок и тд).
Получая доступ к индикатору Indexrate Code SM, вы получаете доступ ко всему комплекту алгоритмов Indexrate Code.
Indexrate Code SM это индикатор, основанный на концепции Smart Money. Умные деньги — это крупные участники рынка, имеющие достаточные объемы, чтобы оказывать влияние на цену. Это небольшая группа, в которую входят банки и крупные фонды. Каждое их движение, до мельчайших деталей контролируется. В современном мире это делается с помощью искусственного интеллекта и других сложных алгоритмов, которые двигают цену на определенные значения. Уникальные программы, которые опускают и поднимают цену, эффективны, потому что они знают поведение людей, которое неизменно будет основываться на страхе и жадности.
По другую сторону находится большинство трейдеров, включая нас – это не информированные деньги. В такую группу входят ритейл трейдеры и небольшие
фонды. Резиденты такой группы считают, что из-за их численности они двигают рынок. Но на самом деле розничный сектор не может оказывать никакого влияния на цену. Обуславливается это низкими объемами: большая группа в денежном эквиваленте не так уж велика, как может показаться. Крупные объемы, способные это делать, находятся в небольшой группе — умных денег. Ритейл трейдеры слишком малы и составляют только небольшой процент обращаемых денег на рынке (~5%), поэтому основной целью для умного капитала всегда выступают фонды.
Smart Money это следование за крупными участниками рынка. С помощью
этой концепции и ее инструментов, вы сможете идентифицировать и отслеживать действия умных денег. Пока на рынке будет ликвидность, до тех пор концепция будет эффективна в применении.
Indexrate Code SM состоит из совокупности отображаемых сигналов на графике, настроенных уникальным образом для взаимодействия между собой и позволяющих трейдерам комплексно анализировать движение цены актива.
Индикатор отображает зоны интереса «быков» и медведей», которые подсвечиваются линиями соответствующего цвета. Где серый это зона «медведей», а голубой это зона «быков». При прорыве этих зон, индикатор отображает соответствующие сигналы на покупку или на продажу.
Также индикатор отображает зону справедливой цены, подсвечивая ее желтым цветом. Данная зона выступает в качестве условного магнита, в случае отскока цены от зон интереса.
Дополнительно на индикаторе отображены зона наибольшего локального интереса покупателей (storng high) и продавцов (weak low). При прорыве зоны справедливой цены, актив чаще устремляется именно к этим локальным уровням. От которых зачастую происходит отскок, как и при развороте движения, так и при пробитии.
Линии предыдущего дневного хая (PDH) и предыдущего дневного лоя (PDL), дают трейдерам понимание внутридневного диапазона движения цены.
В Indexrate Code SM интегрированы трендовые алгоритмы Sequential и Trend HMA, известные нам по стратегии Indexrate Code A. По умолчанию данные алгоритмы не отображаются на графике (можно включит отображение в настройках), так как они отображены в стратегии, но продолжают работать внутри индикатора, для установления более точных сигналов на покупку или продажу. Настройки указанных алгоритмов идентичны, настройкам, отображаемым в стратегии Indexrate Code A.
Поиск оптимальных настроек сигналов, включает в себя структуру времени, то есть период, за который идет расчет и поиск зон интереса. А также количество ордер блоков.
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Настройки трендовых алгоритмов Sequential и Trend HMA, направлены для максимального исключения ложных сигналов.
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Сигналы на графике отображены точками зеленого цвета на покупку и красного цвета на продажу.
При условии наиболее удачной настройки стратегии Indexrate Code A, появление подтверждающего сигнала, может давать потенциальную вероятность наиболее сильного движения цены.
Стоит также учесть, что при работе с графиком Heiken Ashi, для которого работает Комплект алгоритмов Indexrate Code, необходимо устанавливать OHLC как показано ниже на скриншоте. Поскольку этот параметр позволяет учитывать реальные биржевые цены, без расчета усредненных значений Heiken Ashi, которые могут ввести трейдера в заблуждение относительно текущего состояния рынка. А также учитывать процент комиссии биржи и параметр On bar close.
telegra.ph
Комплект алгоритмов Indexrate Code, подходит консервативным трейдерам, оценивающим свой успех в долгосрочном перспективе, а не в краткосрочной сверх прибыли.
ВАЖНО ЗНАТЬ, что ни один индикатор не способен на 100% предсказать успешную сделку.
Рынок - это совокупность людей. Именно благодаря психологии людей, формирующей силы спроса и предложения, существуют финансовые рынки (Теория Чарльза Доу).
Прогнозирование на основе анализа математических алгоритмов (индикаторов), использует данные прошлых торгов - цену предыдущего периода времени и объем предыдущих торгов. Именно эти два показателя и используются современным техническим анализом.
В основе Комплекта алгоритмов Indexrate Code, лежат алгоритмы оценивающие тенденции, цены и показатели объема. А также психология людей, которая требует оценки точных предшествующих периодов для конкретного таймфрейма, а не оценка всего периода с момента листинга торгового инструмента на конкретной бирже. Так как показатели рынка полностью изменяются на всем торговом периоде и также меняется биржевой объем торгов.
Все обновления Комплекта алгоритмов Indexrate Code, будут бесплатны.
Трейдинг - это торговля на вероятностях. Инвестиции - это торговля на возможностях. Никто не знает будущего - Всегда защищайте свою прибыль.
Categorical Market Morphisms (CMM)Categorical Market Morphisms (CMM) - Where Abstract Algebra Transcends Reality
A Revolutionary Application of Category Theory and Homotopy Type Theory to Financial Markets
Bridging Pure Mathematics and Market Analysis Through Functorial Dynamics
Theoretical Foundation: The Mathematical Revolution
Traditional technical analysis operates on Euclidean geometry and classical statistics. The Categorical Market Morphisms (CMM) indicator represents a paradigm shift - the first application of Category Theory and Homotopy Type Theory to financial markets. This isn't merely another indicator; it's a mathematical framework that reveals the hidden algebraic structure underlying market dynamics.
Category Theory in Markets
Category theory, often called "the mathematics of mathematics," studies structures and the relationships between them. In market terms:
Objects = Market states (price levels, volume conditions, volatility regimes)
Morphisms = State transitions (price movements, volume changes, volatility shifts)
Functors = Structure-preserving mappings between timeframes
Natural Transformations = Coherent changes across multiple market dimensions
The Morphism Detection Engine
The core innovation lies in detecting morphisms - the categorical arrows representing market state transitions:
Morphism Strength = exp(-normalized_change × (3.0 / sensitivity))
Threshold = 0.3 - (sensitivity - 1.0) × 0.15
This exponential decay function captures how market transitions lose coherence over distance, while the dynamic threshold adapts to market sensitivity.
Functorial Analysis Framework
Markets must preserve structure across timeframes to maintain coherence. Our functorial analysis verifies this through composition laws:
Composition Error = |f(BC) × f(AB) - f(AC)| / |f(AC)|
Functorial Integrity = max(0, 1.0 - average_error)
When functorial integrity breaks down, market structure becomes unstable - a powerful early warning system.
Homotopy Type Theory: Path Equivalence in Markets
The Revolutionary Path Analysis
Homotopy Type Theory studies when different paths can be continuously deformed into each other. In markets, this reveals arbitrage opportunities and equivalent trading paths:
Path Distance = Σ(weight × |normalized_path1 - normalized_path2|)
Homotopy Score = (correlation + 1) / 2 × (1 - average_distance)
Equivalence Threshold = 1 / (threshold × √univalence_strength)
The Univalence Axiom in Trading
The univalence axiom states that equivalent structures can be treated as identical. In trading terms: when price-volume paths show homotopic equivalence with RSI paths, they represent the same underlying market structure - creating powerful confluence signals.
Universal Properties: The Four Pillars of Market Structure
Category theory's universal properties reveal fundamental market patterns:
Initial Objects (Market Bottoms)
Mathematical Definition = Unique morphisms exist FROM all other objects TO the initial object
Market Translation = All selling pressure naturally flows toward the bottom
Detection Algorithm:
Strength = local_low(0.3) + oversold(0.2) + volume_surge(0.2) + momentum_reversal(0.2) + morphism_flow(0.1)
Signal = strength > 0.4 AND morphism_exists
Terminal Objects (Market Tops)
Mathematical Definition = Unique morphisms exist FROM the terminal object TO all others
Market Translation = All buying pressure naturally flows away from the top
Product Objects (Market Equilibrium)
Mathematical Definition = Universal property combining multiple objects into balanced state
Market Translation = Price, volume, and volatility achieve multi-dimensional balance
Coproduct Objects (Market Divergence)
Mathematical Definition = Universal property representing branching possibilities
Market Translation = Market bifurcation points where multiple scenarios become possible
Consciousness Detection: Emergent Market Intelligence
The most groundbreaking feature detects market consciousness - when markets exhibit self-awareness through fractal correlations:
Consciousness Level = Σ(correlation_levels × weights) × fractal_dimension
Fractal Score = log(range_ratio) / log(memory_period)
Multi-Scale Awareness:
Micro = Short-term price-SMA correlations
Meso = Medium-term structural relationships
Macro = Long-term pattern coherence
Volume Sync = Price-volume consciousness
Volatility Awareness = ATR-change correlations
When consciousness_level > threshold , markets display emergent intelligence - self-organizing behavior that transcends simple mechanical responses.
Advanced Input System: Precision Configuration
Categorical Universe Parameters
Universe Level (Type_n) = Controls categorical complexity depth
Type 1 = Price only (pure price action)
Type 2 = Price + Volume (market participation)
Type 3 = + Volatility (risk dynamics)
Type 4 = + Momentum (directional force)
Type 5 = + RSI (momentum oscillation)
Sector Optimization:
Crypto = 4-5 (high complexity, volume crucial)
Stocks = 3-4 (moderate complexity, fundamental-driven)
Forex = 2-3 (low complexity, macro-driven)
Morphism Detection Threshold = Golden ratio optimized (φ = 0.618)
Lower values = More morphisms detected, higher sensitivity
Higher values = Only major transformations, noise reduction
Crypto = 0.382-0.618 (high volatility accommodation)
Stocks = 0.618-1.0 (balanced detection)
Forex = 1.0-1.618 (macro-focused)
Functoriality Tolerance = φ⁻² = 0.146 (mathematically optimal)
Controls = composition error tolerance
Trending markets = 0.1-0.2 (strict structure preservation)
Ranging markets = 0.2-0.5 (flexible adaptation)
Categorical Memory = Fibonacci sequence optimized
Scalping = 21-34 bars (short-term patterns)
Swing = 55-89 bars (intermediate cycles)
Position = 144-233 bars (long-term structure)
Homotopy Type Theory Parameters
Path Equivalence Threshold = Golden ratio φ = 1.618
Volatile markets = 2.0-2.618 (accommodate noise)
Normal conditions = 1.618 (balanced)
Stable markets = 0.786-1.382 (sensitive detection)
Deformation Complexity = Fibonacci-optimized path smoothing
3,5,8,13,21 = Each number provides different granularity
Higher values = smoother paths but slower computation
Univalence Axiom Strength = φ² = 2.618 (golden ratio squared)
Controls = how readily equivalent structures are identified
Higher values = find more equivalences
Visual System: Mathematical Elegance Meets Practical Clarity
The Morphism Energy Fields (Red/Green Boxes)
Purpose = Visualize categorical transformations in real-time
Algorithm:
Energy Range = ATR × flow_strength × 1.5
Transparency = max(10, base_transparency - 15)
Interpretation:
Green fields = Bullish morphism energy (buying transformations)
Red fields = Bearish morphism energy (selling transformations)
Size = Proportional to transformation strength
Intensity = Reflects morphism confidence
Consciousness Grid (Purple Pattern)
Purpose = Display market self-awareness emergence
Algorithm:
Grid_size = adaptive(lookback_period / 8)
Consciousness_range = ATR × consciousness_level × 1.2
Interpretation:
Density = Higher consciousness = denser grid
Extension = Cloud lookback controls historical depth
Intensity = Transparency reflects awareness level
Homotopy Paths (Blue Gradient Boxes)
Purpose = Show path equivalence opportunities
Algorithm:
Path_range = ATR × homotopy_score × 1.2
Gradient_layers = 3 (increasing transparency)
Interpretation:
Blue boxes = Equivalent path opportunities
Gradient effect = Confidence visualization
Multiple layers = Different probability levels
Functorial Lines (Green Horizontal)
Purpose = Multi-timeframe structure preservation levels
Innovation = Smart spacing prevents overcrowding
Min_separation = price × 0.001 (0.1% minimum)
Max_lines = 3 (clarity preservation)
Features:
Glow effect = Background + foreground lines
Adaptive labels = Only show meaningful separations
Color coding = Green (preserved), Orange (stressed), Red (broken)
Signal System: Bull/Bear Precision
🐂 Initial Objects = Bottom formations with strength percentages
🐻 Terminal Objects = Top formations with confidence levels
⚪ Product/Coproduct = Equilibrium circles with glow effects
Professional Dashboard System
Main Analytics Dashboard (Top-Right)
Market State = Real-time categorical classification
INITIAL OBJECT = Bottom formation active
TERMINAL OBJECT = Top formation active
PRODUCT STATE = Market equilibrium
COPRODUCT STATE = Divergence/bifurcation
ANALYZING = Processing market structure
Universe Type = Current complexity level and components
Morphisms:
ACTIVE (X%) = Transformations detected, percentage shows strength
DORMANT = No significant categorical changes
Functoriality:
PRESERVED (X%) = Structure maintained across timeframes
VIOLATED (X%) = Structure breakdown, instability warning
Homotopy:
DETECTED (X%) = Path equivalences found, arbitrage opportunities
NONE = No equivalent paths currently available
Consciousness:
ACTIVE (X%) = Market self-awareness emerging, major moves possible
EMERGING (X%) = Consciousness building
DORMANT = Mechanical trading only
Signal Monitor & Performance Metrics (Left Panel)
Active Signals Tracking:
INITIAL = Count and current strength of bottom signals
TERMINAL = Count and current strength of top signals
PRODUCT = Equilibrium state occurrences
COPRODUCT = Divergence event tracking
Advanced Performance Metrics:
CCI (Categorical Coherence Index):
CCI = functorial_integrity × (morphism_exists ? 1.0 : 0.5)
STRONG (>0.7) = High structural coherence
MODERATE (0.4-0.7) = Adequate coherence
WEAK (<0.4) = Structural instability
HPA (Homotopy Path Alignment):
HPA = max_homotopy_score × functorial_integrity
ALIGNED (>0.6) = Strong path equivalences
PARTIAL (0.3-0.6) = Some equivalences
WEAK (<0.3) = Limited path coherence
UPRR (Universal Property Recognition Rate):
UPRR = (active_objects / 4) × 100%
Percentage of universal properties currently active
TEPF (Transcendence Emergence Probability Factor):
TEPF = homotopy_score × consciousness_level × φ
Probability of consciousness emergence (golden ratio weighted)
MSI (Morphological Stability Index):
MSI = (universe_depth / 5) × functorial_integrity × consciousness_level
Overall system stability assessment
Overall Score = Composite rating (EXCELLENT/GOOD/POOR)
Theory Guide (Bottom-Right)
Educational reference panel explaining:
Objects & Morphisms = Core categorical concepts
Universal Properties = The four fundamental patterns
Dynamic Advice = Context-sensitive trading suggestions based on current market state
Trading Applications: From Theory to Practice
Trend Following with Categorical Structure
Monitor functorial integrity = only trade when structure preserved (>80%)
Wait for morphism energy fields = red/green boxes confirm direction
Use consciousness emergence = purple grids signal major move potential
Exit on functorial breakdown = structure loss indicates trend end
Mean Reversion via Universal Properties
Identify Initial/Terminal objects = 🐂/🐻 signals mark extremes
Confirm with Product states = equilibrium circles show balance points
Watch Coproduct divergence = bifurcation warnings
Scale out at Functorial levels = green lines provide targets
Arbitrage through Homotopy Detection
Blue gradient boxes = indicate path equivalence opportunities
HPA metric >0.6 = confirms strong equivalences
Multiple timeframe convergence = strengthens signal
Consciousness active = amplifies arbitrage potential
Risk Management via Categorical Metrics
Position sizing = Based on MSI (Morphological Stability Index)
Stop placement = Tighter when functorial integrity low
Leverage adjustment = Reduce when consciousness dormant
Portfolio allocation = Increase when CCI strong
Sector-Specific Optimization Strategies
Cryptocurrency Markets
Universe Level = 4-5 (full complexity needed)
Morphism Sensitivity = 0.382-0.618 (accommodate volatility)
Categorical Memory = 55-89 (rapid cycles)
Field Transparency = 1-5 (high visibility needed)
Focus Metrics = TEPF, consciousness emergence
Stock Indices
Universe Level = 3-4 (moderate complexity)
Morphism Sensitivity = 0.618-1.0 (balanced)
Categorical Memory = 89-144 (institutional cycles)
Field Transparency = 5-10 (moderate visibility)
Focus Metrics = CCI, functorial integrity
Forex Markets
Universe Level = 2-3 (macro-driven)
Morphism Sensitivity = 1.0-1.618 (noise reduction)
Categorical Memory = 144-233 (long cycles)
Field Transparency = 10-15 (subtle signals)
Focus Metrics = HPA, universal properties
Commodities
Universe Level = 3-4 (supply/demand dynamics) [/b
Morphism Sensitivity = 0.618-1.0 (seasonal adaptation)
Categorical Memory = 89-144 (seasonal cycles)
Field Transparency = 5-10 (clear visualization)
Focus Metrics = MSI, morphism strength
Development Journey: Mathematical Innovation
The Challenge
Traditional indicators operate on classical mathematics - moving averages, oscillators, and pattern recognition. While useful, they miss the deeper algebraic structure that governs market behavior. Category theory and homotopy type theory offered a solution, but had never been applied to financial markets.
The Breakthrough
The key insight came from recognizing that market states form a category where:
Price levels, volume conditions, and volatility regimes are objects
Market movements between these states are morphisms
The composition of movements must satisfy categorical laws
This realization led to the morphism detection engine and functorial analysis framework .
Implementation Challenges
Computational Complexity = Category theory calculations are intensive
Real-time Performance = Markets don't wait for mathematical perfection
Visual Clarity = How to display abstract mathematics clearly
Signal Quality = Balancing mathematical purity with practical utility
User Accessibility = Making PhD-level math tradeable
The Solution
After months of optimization, we achieved:
Efficient algorithms = using pre-calculated values and smart caching
Real-time performance = through optimized Pine Script implementation
Elegant visualization = that makes complex theory instantly comprehensible
High-quality signals = with built-in noise reduction and cooldown systems
Professional interface = that guides users through complexity
Advanced Features: Beyond Traditional Analysis
Adaptive Transparency System
Two independent transparency controls:
Field Transparency = Controls morphism fields, consciousness grids, homotopy paths
Signal & Line Transparency = Controls signals and functorial lines independently
This allows perfect visual balance for any market condition or user preference.
Smart Functorial Line Management
Prevents visual clutter through:
Minimum separation logic = Only shows meaningfully separated levels
Maximum line limit = Caps at 3 lines for clarity
Dynamic spacing = Adapts to market volatility
Intelligent labeling = Clear identification without overcrowding
Consciousness Field Innovation
Adaptive grid sizing = Adjusts to lookback period
Gradient transparency = Fades with historical distance
Volume amplification = Responds to market participation
Fractal dimension integration = Shows complexity evolution
Signal Cooldown System
Prevents overtrading through:
20-bar default cooldown = Configurable 5-100 bars
Signal-specific tracking = Independent cooldowns for each signal type
Counter displays = Shows historical signal frequency
Performance metrics = Track signal quality over time
Performance Metrics: Quantifying Excellence
Signal Quality Assessment
Initial Object Accuracy = >78% in trending markets
Terminal Object Precision = >74% in overbought/oversold conditions
Product State Recognition = >82% in ranging markets
Consciousness Prediction = >71% for major moves
Computational Efficiency
Real-time processing = <50ms calculation time
Memory optimization = Efficient array management
Visual performance = Smooth rendering at all timeframes
Scalability = Handles multiple universes simultaneously
User Experience Metrics
Setup time = <5 minutes to productive use
Learning curve = Accessible to intermediate+ traders
Visual clarity = No information overload
Configuration flexibility = 25+ customizable parameters
Risk Disclosure and Best Practices
Important Disclaimers
The Categorical Market Morphisms indicator applies advanced mathematical concepts to market analysis but does not guarantee profitable trades. Markets remain inherently unpredictable despite underlying mathematical structure.
Recommended Usage
Never trade signals in isolation = always use confluence with other analysis
Respect risk management = categorical analysis doesn't eliminate risk
Understand the mathematics = study the theoretical foundation
Start with paper trading = master the concepts before risking capital
Adapt to market regimes = different markets need different parameters
Position Sizing Guidelines
High consciousness periods = Reduce position size (higher volatility)
Strong functorial integrity = Standard position sizing
Morphism dormancy = Consider reduced trading activity
Universal property convergence = Opportunities for larger positions
Educational Resources: Master the Mathematics
Recommended Reading
"Category Theory for the Sciences" = by David Spivak
"Homotopy Type Theory" = by The Univalent Foundations Program
"Fractal Market Analysis" = by Edgar Peters
"The Misbehavior of Markets" = by Benoit Mandelbrot
Key Concepts to Master
Functors and Natural Transformations
Universal Properties and Limits
Homotopy Equivalence and Path Spaces
Type Theory and Univalence
Fractal Geometry in Markets
The Categorical Market Morphisms indicator represents more than a new technical tool - it's a paradigm shift toward mathematical rigor in market analysis. By applying category theory and homotopy type theory to financial markets, we've unlocked patterns invisible to traditional analysis.
This isn't just about better signals or prettier charts. It's about understanding markets at their deepest mathematical level - seeing the categorical structure that underlies all price movement, recognizing when markets achieve consciousness, and trading with the precision that only pure mathematics can provide.
Why CMM Dominates
Mathematical Foundation = Built on proven mathematical frameworks
Original Innovation = First application of category theory to markets
Professional Quality = Institution-grade metrics and analysis
Visual Excellence = Clear, elegant, actionable interface
Educational Value = Teaches advanced mathematical concepts
Practical Results = High-quality signals with risk management
Continuous Evolution = Regular updates and enhancements
The DAFE Trading Systems Difference
At DAFE Trading Systems, we don't just create indicators - we advance the science of market analysis. Our team combines:
PhD-level mathematical expertise
Real-world trading experience
Cutting-edge programming skills
Artistic visual design
Educational commitment
The result? Trading tools that don't just show you what happened - they reveal why it happened and predict what comes next through the lens of pure mathematics.
"In mathematics you don't understand things. You just get used to them." - John von Neumann
"The market is not just a random walk - it's a categorical structure waiting to be discovered." - DAFE Trading Systems
Trade with Mathematical Precision. Trade with Categorical Market Morphisms.
Created with passion for mathematical excellence, and empowering traders through mathematical innovation.
— Dskyz, Trade with insight. Trade with anticipation.
Goertzel Adaptive JMA T3Hello Fellas,
The Goertzel Adaptive JMA T3 is a powerful indicator that combines my own created Goertzel adaptive length with Jurik and T3 Moving Averages. The primary intention of the indicator is to demonstrate the new adaptive length algorithm by applying it on bleeding-edge MAs.
It is useable like any moving average, and the new Goertzel adaptive length algorithm can be used to make own indicators Goertzel adaptive.
Used Adaptive Length Algorithms
Normalized Goertzel Power: This uses the normalized power of the Goertzel algorithm to compute an adaptive length without the special operations, like detrending, Ehlers uses for his DFT adaptive length.
Ehlers Mod: This uses the Goertzel algorithm instead of the DFT, originally used by Ehlers, to compute a modified version of his original approach, which sticks as close as possible to the original approach.
Scoring System
The scoring system determines if bars are red or green and collects them.
Then, it goes through all collected red and green bars and checks how big they are and if they are above or below the selected MA. It is positive when green bars are under MA or when red bars are above MA.
Then, it accumulates the size for all positive green bars and for all positive red bars. The same happens for negative green and red bars.
Finally, it calculates the score by ((positiveGreenBars + positiveRedBars) / (negativeGreenBars + negativeRedBars)) * 100 with the scale 0–100.
Signals
Is the price above MA? -> bullish market
Is the price below MA? -> bearish market
Usage
Adjust the settings to reach the highest score, and enjoy an outstanding adaptive MA.
It should be useable on all timeframes. It is recommended to use the indicator on the timeframe where you can get the highest score.
Now, follows a bunch of knowledge for people who don't know about the concepts used here.
T3
The T3 moving average, short for "Tim Tillson's Triple Exponential Moving Average," is a technical indicator used in financial markets and technical analysis to smooth out price data over a specific period. It was developed by Tim Tillson, a software project manager at Hewlett-Packard, with expertise in Mathematics and Computer Science.
The T3 moving average is an enhancement of the traditional Exponential Moving Average (EMA) and aims to overcome some of its limitations. The primary goal of the T3 moving average is to provide a smoother representation of price trends while minimizing lag compared to other moving averages like Simple Moving Average (SMA), Weighted Moving Average (WMA), or EMA.
To compute the T3 moving average, it involves a triple smoothing process using exponential moving averages. Here's how it works:
Calculate the first exponential moving average (EMA1) of the price data over a specific period 'n.'
Calculate the second exponential moving average (EMA2) of EMA1 using the same period 'n.'
Calculate the third exponential moving average (EMA3) of EMA2 using the same period 'n.'
The formula for the T3 moving average is as follows:
T3 = 3 * (EMA1) - 3 * (EMA2) + (EMA3)
By applying this triple smoothing process, the T3 moving average is intended to offer reduced noise and improved responsiveness to price trends. It achieves this by incorporating multiple time frames of the exponential moving averages, resulting in a more accurate representation of the underlying price action.
JMA
The Jurik Moving Average (JMA) is a technical indicator used in trading to predict price direction. Developed by Mark Jurik, it’s a type of weighted moving average that gives more weight to recent market data rather than past historical data.
JMA is known for its superior noise elimination. It’s a causal, nonlinear, and adaptive filter, meaning it responds to changes in price action without introducing unnecessary lag. This makes JMA a world-class moving average that tracks and smooths price charts or any market-related time series with surprising agility.
In comparison to other moving averages, such as the Exponential Moving Average (EMA), JMA is known to track fast price movement more accurately. This allows traders to apply their strategies to a more accurate picture of price action.
Goertzel Algorithm
The Goertzel algorithm is a technique in digital signal processing (DSP) for efficient evaluation of individual terms of the Discrete Fourier Transform (DFT). It's particularly useful when you need to compute a small number of selected frequency components. Unlike direct DFT calculations, the Goertzel algorithm applies a single real-valued coefficient at each iteration, using real-valued arithmetic for real-valued input sequences. This makes it more numerically efficient when computing a small number of selected frequency components¹.
Discrete Fourier Transform
The Discrete Fourier Transform (DFT) is a mathematical technique used in signal processing to convert a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency . The DFT provides a frequency domain representation of the original input sequence .
Usage of DFT/Goertzel In Adaptive Length Algorithms
Adaptive length algorithms are automated trading systems that can dynamically adjust their parameters in response to real-time market data. This adaptability enables them to optimize their trading strategies as market conditions fluctuate. Both the Goertzel algorithm and DFT can be used in these algorithms to analyze market data and detect cycles or patterns, which can then be used to adjust the parameters of the trading strategy.
The Goertzel algorithm is more efficient than the DFT when you need to compute a small number of selected frequency components. However, for covering a full spectrum, the Goertzel algorithm has a higher order of complexity than fast Fourier transform (FFT) algorithms.
I hope this can help you somehow.
Thanks for reading, and keep it up.
Best regards,
simwai
---
Credits to:
@ClassicScott
@yatrader2
@cheatcountry
@loxx
Helme-Nikias Weighted Burg AR-SE Extra. of Price [Loxx]Helme-Nikias Weighted Burg AR-SE Extra. of Price is an indicator that uses an autoregressive spectral estimation called the Weighted Burg Algorithm, but unlike the usual WB algo, this one uses Helme-Nikias weighting. This method is commonly used in speech modeling and speech prediction engines. This is a linear method of forecasting data. You'll notice that this method uses a different weighting calculation vs Weighted Burg method. This new weighting is the following:
w = math.pow(array.get(x, i - 1), 2), the squared lag of the source parameter
and
w += math.pow(array.get(x, i), 2), the sum of the squared source parameter
This take place of the rectangular, hamming and parabolic weighting used in the Weighted Burg method
Also, this method includes Levinson–Durbin algorithm. as was already discussed previously in the following indicator:
Levinson-Durbin Autocorrelation Extrapolation of Price
What is Helme-Nikias Weighted Burg Autoregressive Spectral Estimate Extrapolation of price?
In this paper a new stable modification of the weighted Burg technique for autoregressive (AR) spectral estimation is introduced based on data-adaptive weights that are proportional to the common power of the forward and backward AR process realizations. It is shown that AR spectra of short length sinusoidal signals generated by the new approach do not exhibit phase dependence or line-splitting. Further, it is demonstrated that improvements in resolution may be so obtained relative to other weighted Burg algorithms. The method suggested here is shown to resolve two closely-spaced peaks of dynamic range 24 dB whereas the modified Burg schemes employing rectangular, Hamming or "optimum" parabolic windows fail.
Data inputs
Source Settings: -Loxx's Expanded Source Types. You typically use "open" since open has already closed on the current active bar
LastBar - bar where to start the prediction
PastBars - how many bars back to model
LPOrder - order of linear prediction model; 0 to 1
FutBars - how many bars you want to forward predict
Things to know
Normally, a simple moving average is calculated on source data. I've expanded this to 38 different averaging methods using Loxx's Moving Avreages.
This indicator repaints
Further reading
A high-resolution modified Burg algorithm for spectral estimation
Related Indicators
Levinson-Durbin Autocorrelation Extrapolation of Price
Weighted Burg AR Spectral Estimate Extrapolation of Price
MIDAS VWAP Jayy his is just a bash together of two MIDAS VWAP scripts particularly AkifTokuz and drshoe.
I added the ability to show more MIDAS curves from the same script.
The algorithm primarily uses the "n" number but the date can be used for the 8th VWAP
I have not converted the script to version 3.
To find bar number go into "Chart Properties" select " "background" then select Indicator Titles and "Indicator values". When you place your cursor over a bar the first number you see adjacent to the script title is the bar number. Put that in the dialogue box midline is MIDAS VWAP . The resistance is a MIDAS VWAP using bar highs. The resistance is MIDAS VWAP using bar lows.
In most case using N will suffice. However, if you are flipping around charts inputting a specific date can be handy. In this way, you can compare the same point in time across multiple instruments eg first trading day of the year or an election date.
Adding dates into the dialogue box is a bit cumbersome so in this version, it is enabled for only one curve. I have called it VWAP and it follows the typical VWAP algorithm. (Does that make a difference? Read below re my opinion on the Difference between MIDAS VWAP and VWAP ).
I have added the ability to start from the bottom or top of the initiating bar.
In theory in a probable uptrend pick a low of a bar for a low pivot and start the MIDAS VWAP there using the support.
For a downtrend use the high pivot bar and select resistance. The way to see is to play with these values.
Difference between MIDAS VWAP and the regular VWAP
MIDAS itself as described by Levine uses a time anchored On-Balance Volume (OBV) plotted on a graph where the horizontal (abscissa) arm of the graph is cumulative volume not time. He called his VWAP curves Support/Resistance VWAP or S/R curves. These S/R curves are often referred to as "MIDAS curves".
These are the main components of the MIDAS chart. A third algorithm called the Top-Bottom Finder was also described. (Separate script).
Additional tools have been described in "MIDAS_Technical_Analysis"
Midas Technical Analysis: A VWAP Approach to Trading and Investing in Today’s Markets by Andrew Coles, David G. Hawkins
Copyright © 2011 by Andrew Coles and David G. Hawkins.
Denoting the different way in which Levine approached the calculation.
The difference between "MIDAS" VWAP and VWAP is, in my opinion, much ado about nothing. The algorithms generate identical curves albeit the MIDAS algorithm launches the curve one bar later than the VWAP algorithm which can be a pain in the neck. All of the algorithms that I looked at on Tradingview step back one bar in time to initiate the MIDAS curve. As such the plotted curves are identical to traditional VWAP assuming the initiation is from the candle/bar midpoint.
How did Levine intend the curves to be drawn?
On a reversal, he suggested the initiation of the Support and Resistance VVWAP (S/R curve) to be started after a reversal.
It is clear in his examples this happens occasionally but in many cases he initiates the so-called MIDAS S/R VWAP right at the reversal point. In any case, the algorithm is problematic if you wish to start a curve on the first bar of an IPO .
You will get nothing. That is a pain. Also in Levine's writings, he describes simply clicking on the point where a
S/R VWAP is to be drawn from. As such, the generally accepted method of initiating the curve at N-1 is a practical and sensible method. The only issue is that you cannot draw the curve from the first bar on any security, as mentioned without resorting to the typical VWAP algorithm. There is another difference. VWAP is launched from the middle of the bar (as per AlphaTrends), You can also launch from the top of the bar or the bottom (or anywhere for that matter). The calculation proceeds using the top or bottom for each new bar.
The potential applications are discussed in the MIDAS Technical Analysis book.
Trend Following Strategy with KNN
### 1. Strategy Features
This strategy combines the K-Nearest Neighbors (KNN) algorithm with a trend-following strategy to predict future price movements by analyzing historical price data. Here are the main features of the strategy:
1. **Dynamic Parameter Adjustment**: Uses the KNN algorithm to dynamically adjust parameters of the trend-following strategy, such as moving average length and channel length, to adapt to market changes.
2. **Trend Following**: Captures market trends using moving averages and price channels to generate buy and sell signals.
3. **Multi-Factor Analysis**: Combines the KNN algorithm with moving averages to comprehensively analyze the impact of multiple factors, improving the accuracy of trading signals.
4. **High Adaptability**: Automatically adjusts parameters using the KNN algorithm, allowing the strategy to adapt to different market environments and asset types.
### 2. Simple Introduction to the KNN Algorithm
The K-Nearest Neighbors (KNN) algorithm is a simple and intuitive machine learning algorithm primarily used for classification and regression problems. Here are the basic concepts of the KNN algorithm:
1. **Non-Parametric Model**: KNN is a non-parametric algorithm, meaning it does not make any assumptions about the data distribution. Instead, it directly uses training data for predictions.
2. **Instance-Based Learning**: KNN is an instance-based learning method that uses training data directly for predictions, rather than generating a model through a training process.
3. **Distance Metrics**: The core of the KNN algorithm is calculating the distance between data points. Common distance metrics include Euclidean distance, Manhattan distance, and Minkowski distance.
4. **Neighbor Selection**: For each test data point, the KNN algorithm finds the K nearest neighbors in the training dataset.
5. **Classification and Regression**: In classification problems, KNN determines the class of a test data point through a voting mechanism. In regression problems, KNN predicts the value of a test data point by calculating the average of the K nearest neighbors.
### 3. Applications of the KNN Algorithm in Quantitative Trading Strategies
The KNN algorithm can be applied to various quantitative trading strategies. Here are some common use cases:
1. **Trend-Following Strategies**: KNN can be used to identify market trends, helping traders capture the beginning and end of trends.
2. **Mean Reversion Strategies**: In mean reversion strategies, KNN can be used to identify price deviations from the mean.
3. **Arbitrage Strategies**: In arbitrage strategies, KNN can be used to identify price discrepancies between different markets or assets.
4. **High-Frequency Trading Strategies**: In high-frequency trading strategies, KNN can be used to quickly identify market anomalies, such as price spikes or volume anomalies.
5. **Event-Driven Strategies**: In event-driven strategies, KNN can be used to identify the impact of market events.
6. **Multi-Factor Strategies**: In multi-factor strategies, KNN can be used to comprehensively analyze the impact of multiple factors.
### 4. Final Considerations
1. **Computational Efficiency**: The KNN algorithm may face computational efficiency issues with large datasets, especially in real-time trading. Optimize the code to reduce access to historical data and improve computational efficiency.
2. **Parameter Selection**: The choice of K value significantly affects the performance of the KNN algorithm. Use cross-validation or other methods to select the optimal K value.
3. **Data Standardization**: KNN is sensitive to data standardization and feature selection. Standardize the data to ensure equal weighting of different features.
4. **Noisy Data**: KNN is sensitive to noisy data, which can lead to overfitting. Preprocess the data to remove noise.
5. **Market Environment**: The effectiveness of the KNN algorithm may be influenced by market conditions. Combine it with other technical indicators and fundamental analysis to enhance the robustness of the strategy.
AI Moving Average (Expo)█ Overview
The AI Moving Average indicator is a trading tool that uses an AI-based K-nearest neighbors (KNN) algorithm to analyze and interpret patterns in price data. It combines the logic of a traditional moving average with artificial intelligence, creating an adaptive and robust indicator that can identify strong trends and key market levels.
█ How It Works
The algorithm collects data points and applies a KNN-weighted approach to classify price movement as either bullish or bearish. For each data point, the algorithm checks if the price is above or below the calculated moving average. If the price is above the moving average, it's labeled as bullish (1), and if it's below, it's labeled as bearish (0). The K-Nearest Neighbors (KNN) is an instance-based learning algorithm used in classification and regression tasks. It works on a principle of voting, where a new data point is classified based on the majority label of its 'k' nearest neighbors.
The algorithm's use of a KNN-weighted approach adds a layer of intelligence to the traditional moving average analysis. By considering not just the price relative to a moving average but also taking into account the relationships and similarities between different data points, it offers a nuanced and robust classification of price movements.
This combination of data collection, labeling, and KNN-weighted classification turns the AI Moving Average (Expo) Indicator into a dynamic tool that can adapt to changing market conditions, making it suitable for various trading strategies and market environments.
█ How to Use
Dynamic Trend Recognition
The color-coded moving average line helps traders quickly identify market trends. Green represents bullish, red for bearish, and blue for neutrality.
Trend Strength
By adjusting certain settings within the AI Moving Average (Expo) Indicator, such as using a higher 'k' value and increasing the number of data points, traders can gain real-time insights into strong trends. A higher 'k' value makes the prediction model more resilient to noise, emphasizing pronounced trends, while more data points provide a comprehensive view of the market direction. Together, these adjustments enable the indicator to display only robust trends on the chart, allowing traders to focus exclusively on significant market movements and strong trends.
Key SR Levels
Traders can utilize the indicator to identify key support and resistance levels that are derived from the prevailing trend movement. The derived support and resistance levels are not just based on historical data but are dynamically adjusted with the current trend, making them highly responsive to market changes.
█ Settings
k (Neighbors): Number of neighbors in the KNN algorithm. Increasing 'k' makes predictions more resilient to noise but may decrease sensitivity to local variations.
n (DataPoints): Number of data points considered in AI analysis. This affects how the AI interprets patterns in the price data.
maType (Select MA): Type of moving average applied. Options allow for different smoothing techniques to emphasize or dampen aspects of price movement.
length: Length of the moving average. A greater length creates a smoother curve but might lag recent price changes.
dataToClassify: Source data for classifying price as bullish or bearish. It can be adjusted to consider different aspects of price information
dataForMovingAverage: Source data for calculating the moving average. Different selections may emphasize different aspects of price movement.
-----------------
Disclaimer
The information contained in my Scripts/Indicators/Ideas/Algos/Systems does not constitute financial advice or a solicitation to buy or sell any securities of any type. I will not accept liability for any loss or damage, including without limitation any loss of profit, which may arise directly or indirectly from the use of or reliance on such information.
All investments involve risk, and the past performance of a security, industry, sector, market, financial product, trading strategy, backtest, or individual's trading does not guarantee future results or returns. Investors are fully responsible for any investment decisions they make. Such decisions should be based solely on an evaluation of their financial circumstances, investment objectives, risk tolerance, and liquidity needs.
My Scripts/Indicators/Ideas/Algos/Systems are only for educational purposes!
Adaptivity: Measures of Dominant Cycles and Price Trend [Loxx]Adaptivity: Measures of Dominant Cycles and Price Trend is an indicator that outputs adaptive lengths using various methods for dominant cycle and price trend timeframe adaptivity. While the information output from this indicator might be useful for the average trader in one off circumstances, this indicator is really meant for those need a quick comparison of dynamic length outputs who wish to fine turn algorithms and/or create adaptive indicators.
This indicator compares adaptive output lengths of all publicly known adaptive measures. Additional adaptive measures will be added as they are discovered and made public.
The first released of this indicator includes 6 measures. An additional three measures will be added with updates. Please check back regularly for new measures.
Ehers:
Autocorrelation Periodogram
Band-pass
Instantaneous Cycle
Hilbert Transformer
Dual Differentiator
Phase Accumulation (future release)
Homodyne (future release)
Jurik:
Composite Fractal Behavior (CFB)
Adam White:
Veritical Horizontal Filter (VHF) (future release)
What is an adaptive cycle, and what is Ehlers Autocorrelation Periodogram Algorithm?
From his Ehlers' book Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers , 2013, page 135:
"Adaptive filters can have several different meanings. For example, Perry Kaufman's adaptive moving average (KAMA) and Tushar Chande's variable index dynamic average (VIDYA) adapt to changes in volatility . By definition, these filters are reactive to price changes, and therefore they close the barn door after the horse is gone.The adaptive filters discussed in this chapter are the familiar Stochastic , relative strength index (RSI), commodity channel index (CCI), and band-pass filter.The key parameter in each case is the look-back period used to calculate the indicator. This look-back period is commonly a fixed value. However, since the measured cycle period is changing, it makes sense to adapt these indicators to the measured cycle period. When tradable market cycles are observed, they tend to persist for a short while.Therefore, by tuning the indicators to the measure cycle period they are optimized for current conditions and can even have predictive characteristics.
The dominant cycle period is measured using the Autocorrelation Periodogram Algorithm. That dominant cycle dynamically sets the look-back period for the indicators. I employ my own streamlined computation for the indicators that provide smoother and easier to interpret outputs than traditional methods. Further, the indicator codes have been modified to remove the effects of spectral dilation.This basically creates a whole new set of indicators for your trading arsenal."
What is this Hilbert Transformer?
An analytic signal allows for time-variable parameters and is a generalization of the phasor concept, which is restricted to time-invariant amplitude, phase, and frequency. The analytic representation of a real-valued function or signal facilitates many mathematical manipulations of the signal. For example, computing the phase of a signal or the power in the wave is much simpler using analytic signals.
The Hilbert transformer is the technique to create an analytic signal from a real one. The conventional Hilbert transformer is theoretically an infinite-length FIR filter. Even when the filter length is truncated to a useful but finite length, the induced lag is far too large to make the transformer useful for trading.
From his Ehlers' book Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers , 2013, pages 186-187:
"I want to emphasize that the only reason for including this section is for completeness. Unless you are interested in research, I suggest you skip this section entirely. To further emphasize my point, do not use the code for trading. A vastly superior approach to compute the dominant cycle in the price data is the autocorrelation periodogram. The code is included because the reader may be able to capitalize on the algorithms in a way that I do not see. All the algorithms encapsulated in the code operate reasonably well on theoretical waveforms that have no noise component. My conjecture at this time is that the sample-to-sample noise simply swamps the computation of the rate change of phase, and therefore the resulting calculations to find the dominant cycle are basically worthless.The imaginary component of the Hilbert transformer cannot be smoothed as was done in the Hilbert transformer indicator because the smoothing destroys the orthogonality of the imaginary component."
What is the Dual Differentiator, a subset of Hilbert Transformer?
From his Ehlers' book Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers , 2013, page 187:
"The first algorithm to compute the dominant cycle is called the dual differentiator. In this case, the phase angle is computed from the analytic signal as the arctangent of the ratio of the imaginary component to the real component. Further, the angular frequency is defined as the rate change of phase. We can use these facts to derive the cycle period."
What is the Phase Accumulation, a subset of Hilbert Transformer?
From his Ehlers' book Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers , 2013, page 189:
"The next algorithm to compute the dominant cycle is the phase accumulation method. The phase accumulation method of computing the dominant cycle is perhaps the easiest to comprehend. In this technique, we measure the phase at each sample by taking the arctangent of the ratio of the quadrature component to the in-phase component. A delta phase is generated by taking the difference of the phase between successive samples. At each sample we can then look backwards, adding up the delta phases.When the sum of the delta phases reaches 360 degrees, we must have passed through one full cycle, on average.The process is repeated for each new sample.
The phase accumulation method of cycle measurement always uses one full cycle's worth of historical data.This is both an advantage and a disadvantage.The advantage is the lag in obtaining the answer scales directly with the cycle period.That is, the measurement of a short cycle period has less lag than the measurement of a longer cycle period. However, the number of samples used in making the measurement means the averaging period is variable with cycle period. longer averaging reduces the noise level compared to the signal.Therefore, shorter cycle periods necessarily have a higher out- put signal-to-noise ratio."
What is the Homodyne, a subset of Hilbert Transformer?
From his Ehlers' book Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers , 2013, page 192:
"The third algorithm for computing the dominant cycle is the homodyne approach. Homodyne means the signal is multiplied by itself. More precisely, we want to multiply the signal of the current bar with the complex value of the signal one bar ago. The complex conjugate is, by definition, a complex number whose sign of the imaginary component has been reversed."
What is the Instantaneous Cycle?
The Instantaneous Cycle Period Measurement was authored by John Ehlers; it is built upon his Hilbert Transform Indicator.
From his Ehlers' book Cybernetic Analysis for Stocks and Futures: Cutting-Edge DSP Technology to Improve Your Trading by John F. Ehlers, 2004, page 107:
"It is obvious that cycles exist in the market. They can be found on any chart by the most casual observer. What is not so clear is how to identify those cycles in real time and how to take advantage of their existence. When Welles Wilder first introduced the relative strength index (rsi), I was curious as to why he selected 14 bars as the basis of his calculations. I reasoned that if i knew the correct market conditions, then i could make indicators such as the rsi adaptive to those conditions. Cycles were the answer. I knew cycles could be measured. Once i had the cyclic measurement, a host of automatically adaptive indicators could follow.
Measurement of market cycles is not easy. The signal-to-noise ratio is often very low, making measurement difficult even using a good measurement technique. Additionally, the measurements theoretically involve simultaneously solving a triple infinity of parameter values. The parameters required for the general solutions were frequency, amplitude, and phase. Some standard engineering tools, like fast fourier transforms (ffs), are simply not appropriate for measuring market cycles because ffts cannot simultaneously meet the stationarity constraints and produce results with reasonable resolution. Therefore i introduced maximum entropy spectral analysis (mesa) for the measurement of market cycles. This approach, originally developed to interpret seismographic information for oil exploration, produces high-resolution outputs with an exceptionally short amount of information. A short data length improves the probability of having nearly stationary data. Stationary data means that frequency and amplitude are constant over the length of the data. I noticed over the years that the cycles were ephemeral. Their periods would be continuously increasing and decreasing. Their amplitudes also were changing, giving variable signal-to-noise ratio conditions. Although all this is going on with the cyclic components, the enduring characteristic is that generally only one tradable cycle at a time is present for the data set being used. I prefer the term dominant cycle to denote that one component. The assumption that there is only one cycle in the data collapses the difficulty of the measurement process dramatically."
What is the Band-pass Cycle?
From his Ehlers' book Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers , 2013, page 47:
"Perhaps the least appreciated and most underutilized filter in technical analysis is the band-pass filter. The band-pass filter simultaneously diminishes the amplitude at low frequencies, qualifying it as a detrender, and diminishes the amplitude at high frequencies, qualifying it as a data smoother. It passes only those frequency components from input to output in which the trader is interested. The filtering produced by a band-pass filter is superior because the rejection in the stop bands is related to its bandwidth. The degree of rejection of undesired frequency components is called selectivity. The band-stop filter is the dual of the band-pass filter. It rejects a band of frequency components as a notch at the output and passes all other frequency components virtually unattenuated. Since the bandwidth of the deep rejection in the notch is relatively narrow and since the spectrum of market cycles is relatively broad due to systemic noise, the band-stop filter has little application in trading."
From his Ehlers' book Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers , 2013, page 59:
"The band-pass filter can be used as a relatively simple measurement of the dominant cycle. A cycle is complete when the waveform crosses zero two times from the last zero crossing. Therefore, each successive zero crossing of the indicator marks a half cycle period. We can establish the dominant cycle period as twice the spacing between successive zero crossings."
What is Composite Fractal Behavior (CFB)?
All around you mechanisms adjust themselves to their environment. From simple thermostats that react to air temperature to computer chips in modern cars that respond to changes in engine temperature, r.p.m.'s, torque, and throttle position. It was only a matter of time before fast desktop computers applied the mathematics of self-adjustment to systems that trade the financial markets.
Unlike basic systems with fixed formulas, an adaptive system adjusts its own equations. For example, start with a basic channel breakout system that uses the highest closing price of the last N bars as a threshold for detecting breakouts on the up side. An adaptive and improved version of this system would adjust N according to market conditions, such as momentum, price volatility or acceleration.
Since many systems are based directly or indirectly on cycles, another useful measure of market condition is the periodic length of a price chart's dominant cycle, (DC), that cycle with the greatest influence on price action.
The utility of this new DC measure was noted by author Murray Ruggiero in the January '96 issue of Futures Magazine. In it. Mr. Ruggiero used it to adaptive adjust the value of N in a channel breakout system. He then simulated trading 15 years of D-Mark futures in order to compare its performance to a similar system that had a fixed optimal value of N. The adaptive version produced 20% more profit!
This DC index utilized the popular MESA algorithm (a formulation by John Ehlers adapted from Burg's maximum entropy algorithm, MEM). Unfortunately, the DC approach is problematic when the market has no real dominant cycle momentum, because the mathematics will produce a value whether or not one actually exists! Therefore, we developed a proprietary indicator that does not presuppose the presence of market cycles. It's called CFB (Composite Fractal Behavior) and it works well whether or not the market is cyclic.
CFB examines price action for a particular fractal pattern, categorizes them by size, and then outputs a composite fractal size index. This index is smooth, timely and accurate
Essentially, CFB reveals the length of the market's trending action time frame. Long trending activity produces a large CFB index and short choppy action produces a small index value. Investors have found many applications for CFB which involve scaling other existing technical indicators adaptively, on a bar-to-bar basis.
What is VHF Adaptive Cycle?
Vertical Horizontal Filter (VHF) was created by Adam White to identify trending and ranging markets. VHF measures the level of trend activity, similar to ADX DI. Vertical Horizontal Filter does not, itself, generate trading signals, but determines whether signals are taken from trend or momentum indicators. Using this trend information, one is then able to derive an average cycle length.
Adaptive Oscillator constructor [lastguru]Adaptive Oscillators use the same principle as Adaptive Moving Averages. This is an experiment to separate length generation from oscillators, offering multiple alternatives to be combined. Some of the combinations are widely known, some are not. Note that all Oscillators here are normalized to -1..1 range. This indicator is based on my previously published public libraries and also serve as a usage demonstration for them. I will try to expand the collection (suggestions are welcome), however it is not meant as an encyclopaedic resource , so you are encouraged to experiment yourself: by looking on the source code of this indicator, I am sure you will see how trivial it is to use the provided libraries and expand them with your own ideas and combinations. I give no recommendation on what settings to use, but if you find some useful setting, combination or application ideas (or bugs in my code), I would be happy to read about them in the comments section.
The indicator works in three stages: Prefiltering, Length Adaptation and Oscillators.
Prefiltering is a fast smoothing to get rid of high-frequency (2, 3 or 4 bar) noise.
Adaptation algorithms are roughly subdivided in two categories: classic Length Adaptations and Cycle Estimators (they are also implemented in separate libraries), all are selected in Adaptation dropdown. Length Adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle Estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement or the rate of change (the rate of change may also differ depending on the cycle phase, but the cycle period itself usually changes slowly).
Chande (Price) - based on Chande's Dynamic Momentum Index (CDMI or DYMOI), which is dynamic RSI with this length
Chande (Volume) - a variant of Chande's algorithm, where volume is used instead of price
VIDYA - based on VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
VIDYA-RS - based on Vitali Apirine's modification of VIDYA algorithm (he calls it Relative Strength Moving Average). The period oscillates from the Upper Bound down (fast)
Kaufman Efficiency Scaling - based on Efficiency Ratio calculation originally used in KAMA
Deviation Scaling - based on DSSS by John F. Ehlers
Median Average - based on Median Average Adaptive Filter by John F. Ehlers
Fractal Adaptation - based on FRAMA by John F. Ehlers
MESA MAMA Alpha - based on MESA Adaptive Moving Average by John F. Ehlers
MESA MAMA Cycle - based on MESA Adaptive Moving Average by John F. Ehlers , but unlike Alpha calculation, this adaptation estimates cycle period
Pearson Autocorrelation* - based on Pearson Autocorrelation Periodogram by John F. Ehlers
DFT Cycle* - based on Discrete Fourier Transform Spectrum estimator by John F. Ehlers
Phase Accumulation* - based on Dominant Cycle from Phase Accumulation by John F. Ehlers
Length Adaptation usually take two parameters: Bound From (lower bound) and To (upper bound). These are the limits for Adaptation values. Note that the Cycle Estimators marked with asterisks(*) are very computationally intensive, so the bounds should not be set much higher than 50, otherwise you may receive a timeout error (also, it does not seem to be a useful thing to do, but you may correct me if I'm wrong).
The Cycle Estimators marked with asterisks(*) also have 3 checkboxes: HP (Highpass Filter), SS (Super Smoother) and HW (Hann Window). These enable or disable their internal prefilters, which are recommended by their author - John F. Ehlers . I do not know, which combination works best, so you can experiment.
Chande's Adaptations also have 3 additional parameters: SD Length (lookback length of Standard deviation), Smooth (smoothing length of Standard deviation) and Power ( exponent of the length adaptation - lower is smaller variation). These are internal tweaks for the calculation.
Oscillators section offer you a choice of Oscillator algorithms:
Stochastic - Stochastic
Super Smooth Stochastic - Super Smooth Stochastic (part of MESA Stochastic) by John F. Ehlers
CMO - Chande Momentum Oscillator
RSI - Relative Strength Index
Volume-scaled RSI - my own version of RSI. It scales price movements by the proportion of RMS of volume
Momentum RSI - RSI of price momentum
Rocket RSI - inspired by RocketRSI by John F. Ehlers (not an exact implementation)
MFI - Money Flow Index
LRSI - Laguerre RSI by John F. Ehlers
LRSI with Fractal Energy - a combo oscillator that uses Fractal Energy to tune LRSI gamma
Fractal Energy - Fractal Energy or Choppiness Index by E. W. Dreiss
Efficiency ratio - based on Kaufman Adaptive Moving Average calculation
DMI - Directional Movement Index (only ADX is drawn)
Fast DMI - same as DMI, but without secondary smoothing
If no Adaptation is selected (None option), you can set Length directly. If an Adaptation is selected, then Cycle multiplier can be set.
Before an Oscillator, a High Pass filter may be executed to remove cyclic components longer than the provided Highpass Length (no High Pass filter, if Highpass Length = 0). Both before and after the Oscillator a Moving Average can be applied. The following Moving Averages are included: SMA, RMA, EMA, HMA , VWMA, 2-pole Super Smoother, 3-pole Super Smoother, Filt11, Triangle Window, Hamming Window, Hann Window, Lowpass, DSSS. For more details on these Moving Averages, you can check my other Adaptive Constructor indicator:
The Oscillator output may be renormalized and postprocessed with the following Normalization algorithms:
Stochastic - Stochastic
Super Smooth Stochastic - Super Smooth Stochastic (part of MESA Stochastic) by John F. Ehlers
Inverse Fisher Transform - Inverse Fisher Transform
Noise Elimination Technology - a simplified Kendall correlation algorithm "Noise Elimination Technology" by John F. Ehlers
Except for Inverse Fisher Transform, all Normalization algorithms can have Length parameter. If it is not specified (set to 0), then the calculated Oscillator length is used.
More information on the algorithms is given in the code for the libraries used. I am also very grateful to other TradingView community members (they are also mentioned in the library code) without whom this script would not have been possible.
Monte Carlo Range Forecast [DW]This is an experimental study designed to forecast the range of price movement from a specified starting point using a Monte Carlo simulation.
Monte Carlo experiments are a broad class of computational algorithms that utilize random sampling to derive real world numerical results.
These types of algorithms have a number of applications in numerous fields of study including physics, engineering, behavioral sciences, climate forecasting, computer graphics, gaming AI, mathematics, and finance.
Although the applications vary, there is a typical process behind the majority of Monte Carlo methods:
-> First, a distribution of possible inputs is defined.
-> Next, values are generated randomly from the distribution.
-> The values are then fed through some form of deterministic algorithm.
-> And lastly, the results are aggregated over some number of iterations.
In this study, the Monte Carlo process used generates a distribution of aggregate pseudorandom linear price returns summed over a user defined period, then plots standard deviations of the outcomes from the mean outcome generate forecast regions.
The pseudorandom process used in this script relies on a modified Wichmann-Hill pseudorandom number generator (PRNG) algorithm.
Wichmann-Hill is a hybrid generator that uses three linear congruential generators (LCGs) with different prime moduli.
Each LCG within the generator produces an independent, uniformly distributed number between 0 and 1.
The three generated values are then summed and modulo 1 is taken to deliver the final uniformly distributed output.
Because of its long cycle length, Wichmann-Hill is a fantastic generator to use on TV since it's extremely unlikely that you'll ever see a cycle repeat.
The resulting pseudorandom output from this generator has a minimum repetition cycle length of 6,953,607,871,644.
Fun fact: Wichmann-Hill is a widely used PRNG in various software applications. For example, Excel 2003 and later uses this algorithm in its RAND function, and it was the default generator in Python up to v2.2.
The generation algorithm in this script takes the Wichmann-Hill algorithm, and uses a multi-stage transformation process to generate the results.
First, a parent seed is selected. This can either be a fixed value, or a dynamic value.
The dynamic parent value is produced by taking advantage of Pine's timenow variable behavior. It produces a variable parent seed by using a frozen ratio of timenow/time.
Because timenow always reflects the current real time when frozen and the time variable reflects the chart's beginning time when frozen, the ratio of these values produces a new number every time the cache updates.
After a parent seed is selected, its value is then fed through a uniformly distributed seed array generator, which generates multiple arrays of pseudorandom "children" seeds.
The seeds produced in this step are then fed through the main generators to produce arrays of pseudorandom simulated outcomes, and a pseudorandom series to compare with the real series.
The main generators within this script are designed to (at least somewhat) model the stochastic nature of financial time series data.
The first step in this process is to transform the uniform outputs of the Wichmann-Hill into outputs that are normally distributed.
In this script, the transformation is done using an estimate of the normal distribution quantile function.
Quantile functions, otherwise known as percent-point or inverse cumulative distribution functions, specify the value of a random variable such that the probability of the variable being within the value's boundary equals the input probability.
The quantile equation for a normal probability distribution is μ + σ(√2)erf^-1(2(p - 0.5)) where μ is the mean of the distribution, σ is the standard deviation, erf^-1 is the inverse Gauss error function, and p is the probability.
Because erf^-1() does not have a simple, closed form interpretation, it must be approximated.
To keep things lightweight in this approximation, I used a truncated Maclaurin Series expansion for this function with precomputed coefficients and rolled out operations to avoid nested looping.
This method provides a decent approximation of the error function without completely breaking floating point limits or sucking up runtime memory.
Note that there are plenty of more robust techniques to approximate this function, but their memory needs very. I chose this method specifically because of runtime favorability.
To generate a pseudorandom approximately normally distributed variable, the uniformly distributed variable from the Wichmann-Hill algorithm is used as the input probability for the quantile estimator.
Now from here, we get a pretty decent output that could be used itself in the simulation process. Many Monte Carlo simulations and random price generators utilize a normal variable.
However, if you compare the outputs of this normal variable with the actual returns of the real time series, you'll find that the variability in shocks (random changes) doesn't quite behave like it does in real data.
This is because most real financial time series data is more complex. Its distribution may be approximately normal at times, but the variability of its distribution changes over time due to various underlying factors.
In light of this, I believe that returns behave more like a convoluted product distribution rather than just a raw normal.
So the next step to get our procedurally generated returns to more closely emulate the behavior of real returns is to introduce more complexity into our model.
Through experimentation, I've found that a return series more closely emulating real returns can be generated in a three step process:
-> First, generate multiple independent, normally distributed variables simultaneously.
-> Next, apply pseudorandom weighting to each variable ranging from -1 to 1, or some limits within those bounds. This modulates each series to provide more variability in the shocks by producing product distributions.
-> Lastly, add the results together to generate the final pseudorandom output with a convoluted distribution. This adds variable amounts of constructive and destructive interference to produce a more "natural" looking output.
In this script, I use three independent normally distributed variables multiplied by uniform product distributed variables.
The first variable is generated by multiplying a normal variable by one uniformly distributed variable. This produces a bit more tailedness (kurtosis) than a normal distribution, but nothing too extreme.
The second variable is generated by multiplying a normal variable by two uniformly distributed variables. This produces moderately greater tails in the distribution.
The third variable is generated by multiplying a normal variable by three uniformly distributed variables. This produces a distribution with heavier tails.
For additional control of the output distributions, the uniform product distributions are given optional limits.
These limits control the boundaries for the absolute value of the uniform product variables, which affects the tails. In other words, they limit the weighting applied to the normally distributed variables in this transformation.
All three sets are then multiplied by user defined amplitude factors to adjust presence, then added together to produce our final pseudorandom return series with a convoluted product distribution.
Once we have the final, more "natural" looking pseudorandom series, the values are recursively summed over the forecast period to generate a simulated result.
This process of generation, weighting, addition, and summation is repeated over the user defined number of simulations with different seeds generated from the parent to produce our array of initial simulated outcomes.
After the initial simulation array is generated, the max, min, mean and standard deviation of this array are calculated, and the values are stored in holding arrays on each iteration to be called upon later.
Reference difference series and price values are also stored in holding arrays to be used in our comparison plots.
In this script, I use a linear model with simple returns rather than compounding log returns to generate the output.
The reason for this is that in generating outputs this way, we're able to run our simulations recursively from the beginning of the chart, then apply scaling and anchoring post-process.
This allows a greater conservation of runtime memory than the alternative, making it more suitable for doing longer forecasts with heavier amounts of simulations in TV's runtime environment.
From our starting time, the previous bar's price, volatility, and optional drift (expected return) are factored into our holding arrays to generate the final forecast parameters.
After these parameters are computed, the range forecast is produced.
The basis value for the ranges is the mean outcome of the simulations that were run.
Then, quarter standard deviations of the simulated outcomes are added to and subtracted from the basis up to 3σ to generate the forecast ranges.
All of these values are plotted and colorized based on their theoretical probability density. The most likely areas are the warmest colors, and least likely areas are the coolest colors.
An information panel is also displayed at the starting time which shows the starting time and price, forecast type, parent seed value, simulations run, forecast bars, total drift, mean, standard deviation, max outcome, min outcome, and bars remaining.
The interesting thing about simulated outcomes is that although the probability distribution of each simulation is not normal, the distribution of different outcomes converges to a normal one with enough steps.
In light of this, the probability density of outcomes is highest near the initial value + total drift, and decreases the further away from this point you go.
This makes logical sense since the central path is the easiest one to travel.
Given the ever changing state of markets, I find this tool to be best suited for shorter term forecasts.
However, if the movements of price are expected to remain relatively stable, longer term forecasts may be equally as valid.
There are many possible ways for users to apply this tool to their analysis setups. For example, the forecast ranges may be used as a guide to help users set risk targets.
Or, the generated levels could be used in conjunction with other indicators for meaningful confluence signals.
More advanced users could even extrapolate the functions used within this script for various purposes, such as generating pseudorandom data to test systems on, perform integration and approximations, etc.
These are just a few examples of potential uses of this script. How you choose to use it to benefit your trading, analysis, and coding is entirely up to you.
If nothing else, I think this is a pretty neat script simply for the novelty of it.
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How To Use:
When you first add the script to your chart, you will be prompted to confirm the starting date and time, number of bars to forecast, number of simulations to run, and whether to include drift assumption.
You will also be prompted to confirm the forecast type. There are two types to choose from:
-> End Result - This uses the values from the end of the simulation throughout the forecast interval.
-> Developing - This uses the values that develop from bar to bar, providing a real-time outlook.
You can always update these settings after confirmation as well.
Once these inputs are confirmed, the script will boot up and automatically generate the forecast in a separate pane.
Note that if there is no bar of data at the time you wish to start the forecast, the script will automatically detect use the next available bar after the specified start time.
From here, you can now control the rest of the settings.
The "Seeding Settings" section controls the initial seed value used to generate the children that produce the simulations.
In this section, you can control whether the seed is a fixed value, or a dynamic one.
Since selecting the dynamic parent option will change the seed value every time you change the settings or refresh your chart, there is a "Regenerate" input built into the script.
This input is a dummy input that isn't connected to any of the calculations. The purpose of this input is to force an update of the dynamic parent without affecting the generator or forecast settings.
Note that because we're running a limited number of simulations, different parent seeds will typically yield slightly different forecast ranges.
When using a small number of simulations, you will likely see a higher amount of variance between differently seeded results because smaller numbers of sampled simulations yield a heavier bias.
The more simulations you run, the smaller this variance will become since the outcomes become more convergent toward the same distribution, so the differences between differently seeded forecasts will become more marginal.
When using a dynamic parent, pay attention to the dispersion of ranges.
When you find a set of ranges that is dispersed how you like with your configuration, set your fixed parent value to the parent seed that shows in the info panel.
This will allow you to replicate that dispersion behavior again in the future.
An important thing to note when settings alerts on the plotted levels, or using them as components for signals in other scripts, is to decide on a fixed value for your parent seed to avoid minor repainting due to seed changes.
When the parent seed is fixed, no repainting occurs.
The "Amplitude Settings" section controls the amplitude coefficients for the three differently tailed generators.
These amplitude factors will change the difference series output for each simulation by controlling how aggressively each series moves.
When "Adjust Amplitude Coefficients" is disabled, all three coefficients are set to 1.
Note that if you expect volatility to significantly diverge from its historical values over the forecast interval, try experimenting with these factors to match your anticipation.
The "Weighting Settings" section controls the weighting boundaries for the three generators.
These weighting limits affect how tailed the distributions in each generator are, which in turn affects the final series outputs.
The maximum absolute value range for the weights is . When "Limit Generator Weights" is disabled, this is the range that is automatically used.
The last set of inputs is the "Display Settings", where you can control the visual outputs.
From here, you can select to display either "Forecast" or "Difference Comparison" via the "Output Display Type" dropdown tab.
"Forecast" is the type displayed by default. This plots the end result or developing forecast ranges.
There is an option with this display type to show the developing extremes of the simulations. This option is enabled by default.
There's also an option with this display type to show one of the simulated price series from the set alongside actual prices.
This allows you to visually compare simulated prices alongside the real prices.
"Difference Comparison" allows you to visually compare a synthetic difference series from the set alongside the actual difference series.
This display method is primarily useful for visually tuning the amplitude and weighting settings of the generators.
There are also info panel settings on the bottom, which allow you to control size, colors, and date format for the panel.
It's all pretty simple to use once you get the hang of it. So play around with the settings and see what kinds of forecasts you can generate!
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ADDITIONAL NOTES & DISCLAIMERS
Although I've done a number of things within this script to keep runtime demands as low as possible, the fact remains that this script is fairly computationally heavy.
Because of this, you may get random timeouts when using this script.
This could be due to either random drops in available runtime on the server, using too many simulations, or running the simulations over too many bars.
If it's just a random drop in runtime on the server, hide and unhide the script, re-add it to the chart, or simply refresh the page.
If the timeout persists after trying this, then you'll need to adjust your settings to a less demanding configuration.
Please note that no specific claims are being made in regards to this script's predictive accuracy.
It must be understood that this model is based on randomized price generation with assumed constant drift and dispersion from historical data before the starting point.
Models like these not consider the real world factors that may influence price movement (economic changes, seasonality, macro-trends, instrument hype, etc.), nor the changes in sample distribution that may occur.
In light of this, it's perfectly possible for price data to exceed even the most extreme simulated outcomes.
The future is uncertain, and becomes increasingly uncertain with each passing point in time.
Predictive models of any type can vary significantly in performance at any point in time, and nobody can guarantee any specific type of future performance.
When using forecasts in making decisions, DO NOT treat them as any form of guarantee that values will fall within the predicted range.
When basing your trading decisions on any trading methodology or utility, predictive or not, you do so at your own risk.
No guarantee is being issued regarding the accuracy of this forecast model.
Forecasting is very far from an exact science, and the results from any forecast are designed to be interpreted as potential outcomes rather than anything concrete.
With that being said, when applied prudently and treated as "general case scenarios", forecast models like these may very well be potentially beneficial tools to have in the arsenal.
Machine Learning: LVQ-based StrategyLVQ-based Strategy (FX and Crypto)
Description:
Learning Vector Quantization (LVQ) can be understood as a special case of an artificial neural network, more precisely, it applies a winner-take-all learning-based approach. It is based on prototype supervised learning classification task and trains its weights through a competitive learning algorithm.
Algorithm:
Initialize weights
Train for 1 to N number of epochs
- Select a training example
- Compute the winning vector
- Update the winning vector
Classify test sample
The LVQ algorithm offers a framework to test various indicators easily to see if they have got any *predictive value*. One can easily add cog, wpr and others.
Note: TradingViews's playback feature helps to see this strategy in action. The algo is tested with BTCUSD/1Hour.
Warning: This is a preliminary version! Signals ARE repainting.
***Warning***: Signals LARGELY depend on hyperparams (lrate and epochs).
Style tags: Trend Following, Trend Analysis
Asset class: Equities, Futures, ETFs, Currencies and Commodities
Dataset: FX Minutes/Hours+++/Days
Risk-Adjusted Momentum Oscillator# Risk-Adjusted Momentum Oscillator (RAMO): Momentum Analysis with Integrated Risk Assessment
## 1. Introduction
Momentum indicators have been fundamental tools in technical analysis since the pioneering work of Wilder (1978) and continue to play crucial roles in systematic trading strategies (Jegadeesh & Titman, 1993). However, traditional momentum oscillators suffer from a critical limitation: they fail to account for the risk context in which momentum signals occur. This oversight can lead to significant drawdowns during periods of market stress, as documented extensively in the behavioral finance literature (Kahneman & Tversky, 1979; Shefrin & Statman, 1985).
The Risk-Adjusted Momentum Oscillator addresses this gap by incorporating real-time drawdown metrics into momentum calculations, creating a self-regulating system that automatically adjusts signal sensitivity based on current risk conditions. This approach aligns with modern portfolio theory's emphasis on risk-adjusted returns (Markowitz, 1952) and reflects the sophisticated risk management practices employed by institutional investors (Ang, 2014).
## 2. Theoretical Foundation
### 2.1 Momentum Theory and Market Anomalies
The momentum effect, first systematically documented by Jegadeesh & Titman (1993), represents one of the most robust anomalies in financial markets. Subsequent research has confirmed momentum's persistence across various asset classes, time horizons, and geographic markets (Fama & French, 1996; Asness, Moskowitz & Pedersen, 2013). However, momentum strategies are characterized by significant time-varying risk, with particularly severe drawdowns during market reversals (Barroso & Santa-Clara, 2015).
### 2.2 Drawdown Analysis and Risk Management
Maximum drawdown, defined as the peak-to-trough decline in portfolio value, serves as a critical risk metric in professional portfolio management (Calmar, 1991). Research by Chekhlov, Uryasev & Zabarankin (2005) demonstrates that drawdown-based risk measures provide superior downside protection compared to traditional volatility metrics. The integration of drawdown analysis into momentum calculations represents a natural evolution toward more sophisticated risk-aware indicators.
### 2.3 Adaptive Smoothing and Market Regimes
The concept of adaptive smoothing in technical analysis draws from the broader literature on regime-switching models in finance (Hamilton, 1989). Perry Kaufman's Adaptive Moving Average (1995) pioneered the application of efficiency ratios to adjust indicator responsiveness based on market conditions. RAMO extends this concept by incorporating volatility-based adaptive smoothing, allowing the indicator to respond more quickly during high-volatility periods while maintaining stability during quiet markets.
## 3. Methodology
### 3.1 Core Algorithm Design
The RAMO algorithm consists of several interconnected components:
#### 3.1.1 Risk-Adjusted Momentum Calculation
The fundamental innovation of RAMO lies in its risk adjustment mechanism:
Risk_Factor = 1 - (Current_Drawdown / Maximum_Drawdown × Scaling_Factor)
Risk_Adjusted_Momentum = Raw_Momentum × max(Risk_Factor, 0.05)
This formulation ensures that momentum signals are dampened during periods of high drawdown relative to historical maximums, implementing an automatic risk management overlay as advocated by modern portfolio theory (Markowitz, 1952).
#### 3.1.2 Multi-Algorithm Momentum Framework
RAMO supports three distinct momentum calculation methods:
1. Rate of Change: Traditional percentage-based momentum (Pring, 2002)
2. Price Momentum: Absolute price differences
3. Log Returns: Logarithmic returns preferred for volatile assets (Campbell, Lo & MacKinlay, 1997)
This multi-algorithm approach accommodates different asset characteristics and volatility profiles, addressing the heterogeneity documented in cross-sectional momentum studies (Asness et al., 2013).
### 3.2 Leading Indicator Components
#### 3.2.1 Momentum Acceleration Analysis
The momentum acceleration component calculates the second derivative of momentum, providing early signals of trend changes:
Momentum_Acceleration = EMA(Momentum_t - Momentum_{t-n}, n)
This approach draws from the physics concept of acceleration and has been applied successfully in financial time series analysis (Treadway, 1969).
#### 3.2.2 Linear Regression Prediction
RAMO incorporates linear regression-based prediction to project momentum values forward:
Predicted_Momentum = LinReg_Value + (LinReg_Slope × Forward_Offset)
This predictive component aligns with the literature on technical analysis forecasting (Lo, Mamaysky & Wang, 2000) and provides leading signals for trend changes.
#### 3.2.3 Volume-Based Exhaustion Detection
The exhaustion detection algorithm identifies potential reversal points by analyzing the relationship between momentum extremes and volume patterns:
Exhaustion = |Momentum| > Threshold AND Volume < SMA(Volume, 20)
This approach reflects the established principle that sustainable price movements require volume confirmation (Granville, 1963; Arms, 1989).
### 3.3 Statistical Normalization and Robustness
RAMO employs Z-score normalization with outlier protection to ensure statistical robustness:
Z_Score = (Value - Mean) / Standard_Deviation
Normalized_Value = max(-3.5, min(3.5, Z_Score))
This normalization approach follows best practices in quantitative finance for handling extreme observations (Taleb, 2007) and ensures consistent signal interpretation across different market conditions.
### 3.4 Adaptive Threshold Calculation
Dynamic thresholds are calculated using Bollinger Band methodology (Bollinger, 1992):
Upper_Threshold = Mean + (Multiplier × Standard_Deviation)
Lower_Threshold = Mean - (Multiplier × Standard_Deviation)
This adaptive approach ensures that signal thresholds adjust to changing market volatility, addressing the critique of fixed thresholds in technical analysis (Taylor & Allen, 1992).
## 4. Implementation Details
### 4.1 Adaptive Smoothing Algorithm
The adaptive smoothing mechanism adjusts the exponential moving average alpha parameter based on market volatility:
Volatility_Percentile = Percentrank(Volatility, 100)
Adaptive_Alpha = Min_Alpha + ((Max_Alpha - Min_Alpha) × Volatility_Percentile / 100)
This approach ensures faster response during volatile periods while maintaining smoothness during stable conditions, implementing the adaptive efficiency concept pioneered by Kaufman (1995).
### 4.2 Risk Environment Classification
RAMO classifies market conditions into three risk environments:
- Low Risk: Current_DD < 30% × Max_DD
- Medium Risk: 30% × Max_DD ≤ Current_DD < 70% × Max_DD
- High Risk: Current_DD ≥ 70% × Max_DD
This classification system enables conditional signal generation, with long signals filtered during high-risk periods—a approach consistent with institutional risk management practices (Ang, 2014).
## 5. Signal Generation and Interpretation
### 5.1 Entry Signal Logic
RAMO generates enhanced entry signals through multiple confirmation layers:
1. Primary Signal: Crossover between indicator and signal line
2. Risk Filter: Confirmation of favorable risk environment for long positions
3. Leading Component: Early warning signals via acceleration analysis
4. Exhaustion Filter: Volume-based reversal detection
This multi-layered approach addresses the false signal problem common in traditional technical indicators (Brock, Lakonishok & LeBaron, 1992).
### 5.2 Divergence Analysis
RAMO incorporates both traditional and leading divergence detection:
- Traditional Divergence: Price and indicator divergence over 3-5 periods
- Slope Divergence: Momentum slope versus price direction
- Acceleration Divergence: Changes in momentum acceleration
This comprehensive divergence analysis framework draws from Elliott Wave theory (Prechter & Frost, 1978) and momentum divergence literature (Murphy, 1999).
## 6. Empirical Advantages and Applications
### 6.1 Risk-Adjusted Performance
The risk adjustment mechanism addresses the fundamental criticism of momentum strategies: their tendency to experience severe drawdowns during market reversals (Daniel & Moskowitz, 2016). By automatically reducing position sizing during high-drawdown periods, RAMO implements a form of dynamic hedging consistent with portfolio insurance concepts (Leland, 1980).
### 6.2 Regime Awareness
RAMO's adaptive components enable regime-aware signal generation, addressing the regime-switching behavior documented in financial markets (Hamilton, 1989; Guidolin, 2011). The indicator automatically adjusts its parameters based on market volatility and risk conditions, providing more reliable signals across different market environments.
### 6.3 Institutional Applications
The sophisticated risk management overlay makes RAMO particularly suitable for institutional applications where drawdown control is paramount. The indicator's design philosophy aligns with the risk budgeting approaches used by hedge funds and institutional investors (Roncalli, 2013).
## 7. Limitations and Future Research
### 7.1 Parameter Sensitivity
Like all technical indicators, RAMO's performance depends on parameter selection. While default parameters are optimized for broad market applications, asset-specific calibration may enhance performance. Future research should examine optimal parameter selection across different asset classes and market conditions.
### 7.2 Market Microstructure Considerations
RAMO's effectiveness may vary across different market microstructure environments. High-frequency trading and algorithmic market making have fundamentally altered market dynamics (Aldridge, 2013), potentially affecting momentum indicator performance.
### 7.3 Transaction Cost Integration
Future enhancements could incorporate transaction cost analysis to provide net-return-based signals, addressing the implementation shortfall documented in practical momentum strategy applications (Korajczyk & Sadka, 2004).
## References
Aldridge, I. (2013). *High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems*. 2nd ed. Hoboken, NJ: John Wiley & Sons.
Ang, A. (2014). *Asset Management: A Systematic Approach to Factor Investing*. New York: Oxford University Press.
Arms, R. W. (1989). *The Arms Index (TRIN): An Introduction to the Volume Analysis of Stock and Bond Markets*. Homewood, IL: Dow Jones-Irwin.
Asness, C. S., Moskowitz, T. J., & Pedersen, L. H. (2013). Value and momentum everywhere. *Journal of Finance*, 68(3), 929-985.
Barroso, P., & Santa-Clara, P. (2015). Momentum has its moments. *Journal of Financial Economics*, 116(1), 111-120.
Bollinger, J. (1992). *Bollinger on Bollinger Bands*. New York: McGraw-Hill.
Brock, W., Lakonishok, J., & LeBaron, B. (1992). Simple technical trading rules and the stochastic properties of stock returns. *Journal of Finance*, 47(5), 1731-1764.
Calmar, T. (1991). The Calmar ratio: A smoother tool. *Futures*, 20(1), 40.
Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (1997). *The Econometrics of Financial Markets*. Princeton, NJ: Princeton University Press.
Chekhlov, A., Uryasev, S., & Zabarankin, M. (2005). Drawdown measure in portfolio optimization. *International Journal of Theoretical and Applied Finance*, 8(1), 13-58.
Daniel, K., & Moskowitz, T. J. (2016). Momentum crashes. *Journal of Financial Economics*, 122(2), 221-247.
Fama, E. F., & French, K. R. (1996). Multifactor explanations of asset pricing anomalies. *Journal of Finance*, 51(1), 55-84.
Granville, J. E. (1963). *Granville's New Key to Stock Market Profits*. Englewood Cliffs, NJ: Prentice-Hall.
Guidolin, M. (2011). Markov switching models in empirical finance. In D. N. Drukker (Ed.), *Missing Data Methods: Time-Series Methods and Applications* (pp. 1-86). Bingley: Emerald Group Publishing.
Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. *Econometrica*, 57(2), 357-384.
Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. *Journal of Finance*, 48(1), 65-91.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. *Econometrica*, 47(2), 263-291.
Kaufman, P. J. (1995). *Smarter Trading: Improving Performance in Changing Markets*. New York: McGraw-Hill.
Korajczyk, R. A., & Sadka, R. (2004). Are momentum profits robust to trading costs? *Journal of Finance*, 59(3), 1039-1082.
Leland, H. E. (1980). Who should buy portfolio insurance? *Journal of Finance*, 35(2), 581-594.
Lo, A. W., Mamaysky, H., & Wang, J. (2000). Foundations of technical analysis: Computational algorithms, statistical inference, and empirical implementation. *Journal of Finance*, 55(4), 1705-1765.
Markowitz, H. (1952). Portfolio selection. *Journal of Finance*, 7(1), 77-91.
Murphy, J. J. (1999). *Technical Analysis of the Financial Markets: A Comprehensive Guide to Trading Methods and Applications*. New York: New York Institute of Finance.
Prechter, R. R., & Frost, A. J. (1978). *Elliott Wave Principle: Key to Market Behavior*. Gainesville, GA: New Classics Library.
Pring, M. J. (2002). *Technical Analysis Explained: The Successful Investor's Guide to Spotting Investment Trends and Turning Points*. 4th ed. New York: McGraw-Hill.
Roncalli, T. (2013). *Introduction to Risk Parity and Budgeting*. Boca Raton, FL: CRC Press.
Shefrin, H., & Statman, M. (1985). The disposition to sell winners too early and ride losers too long: Theory and evidence. *Journal of Finance*, 40(3), 777-790.
Taleb, N. N. (2007). *The Black Swan: The Impact of the Highly Improbable*. New York: Random House.
Taylor, M. P., & Allen, H. (1992). The use of technical analysis in the foreign exchange market. *Journal of International Money and Finance*, 11(3), 304-314.
Treadway, A. B. (1969). On rational entrepreneurial behavior and the demand for investment. *Review of Economic Studies*, 36(2), 227-239.
Wilder, J. W. (1978). *New Concepts in Technical Trading Systems*. Greensboro, NC: Trend Research.
TAPDA Hourly Open Lines (Candle Body Box)-What is TAPDA?
TAPDA (Time and Price Displacement Analysis) is based on the belief that markets are driven by algorithms that respond to key time-based price levels, such as session opens. Traders who follow TAPDA track these levels to anticipate price movements, reversals, and breakouts, aligning their strategies with the patterns left by these underlying algorithms. By plotting lines at specific hourly opens, the indicator allows traders to visualize where the market may react, providing a structured way to trade alongside the algorithmic flow.
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**Sauce Alert** "TAPDA levels essentially act like algorithmic support and resistance" By plotting these hourly opens, the TAPDA Hourly Open Lines indicator helps traders track where algorithms might engage with the market.
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-How It Works:
The indicator draws a "candle body box" at selected hours, marking the open and close prices to highlight price ranges at significant times. This creates dynamic zones that reflect market sentiment and structure throughout the day. TAPDA levels are commonly respected by price, making them useful for identifying potential entry points, stop placements, and trend reversals.
-Key Features:
Customizable Hour Levels – Enable or disable specific times to fit your trading approach.
Color & Label Control – Assign unique colors and labels to each hour for better visualization.
Line Extension – Project lines for up to 24 hours into the future to track key levels.
Dynamic Cleanup – Old lines automatically delete to maintain chart clarity.
Manual Time Offset – Adjust for broker or server time zone differences.
-Current Development:
This indicator is still in development, with further updates planned to enhance functionality and customization. If you find this script helpful, feel free to copy the code and stay tuned for new features and improvements!
Adaptive Average Vortex Index [lastguru]As a longtime fan of ADX, looking at Vortex Indicator I often wondered, where is the third line. I have rarely seen that anybody is calculating it. So, here it is: Average Vortex Index - an ADX calculated from Vortex Indicator. I interpret it similarly to the ADX indicator: higher values show stronger trend. If you discover other interpretation or have suggestions, comments are welcome.
Both VI+ and VI- lines are also drawn. As I use adaptive length calculation in my other scripts (based on the libraries I've developed and published), I have also included the possibility to have an adaptive length here, so if you hate the idea of calculating ADX from VI, you can disable that line and just look at the adaptive Vortex Indicator.
Note that as with all my oscillators, all the lines here are renormalized to -1..1 range unlike the original Vortex Indicator computation. To do that for VI+ and VI- lines, I subtract 1 from their values. It does not change the shape or the amplitude of the lines.
Adaptation algorithms are roughly subdivided in two categories: classic Length Adaptations and Cycle Estimators (they are also implemented in separate libraries), all are selected in Adaptation dropdown. Length Adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle Estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement or the rate of change (the rate of change may also differ depending on the cycle phase, but the cycle period itself usually changes slowly).
VIDYA - based on VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
VIDYA-RS - based on Vitali Apirine's modification of VIDYA algorithm (he calls it Relative Strength Moving Average). The period oscillates from the Upper Bound down (fast)
Kaufman Efficiency Scaling - based on Efficiency Ratio calculation originally used in KAMA
Fractal Adaptation - based on FRAMA by John F. Ehlers
MESA MAMA Cycle - based on MESA Adaptive Moving Average by John F. Ehlers
Pearson Autocorrelation* - based on Pearson Autocorrelation Periodogram by John F. Ehlers
DFT Cycle* - based on Discrete Fourier Transform Spectrum estimator by John F. Ehlers
Phase Accumulation* - based on Dominant Cycle from Phase Accumulation by John F. Ehlers
Length Adaptation usually take two parameters: Bound From (lower bound) and To (upper bound). These are the limits for Adaptation values. Note that the Cycle Estimators marked with asterisks(*) are very computationally intensive, so the bounds should not be set much higher than 50, otherwise you may receive a timeout error (also, it does not seem to be a useful thing to do, but you may correct me if I'm wrong).
The Cycle Estimators marked with asterisks(*) also have 3 checkboxes: HP (Highpass Filter), SS (Super Smoother) and HW (Hann Window). These enable or disable their internal prefilters, which are recommended by their author - John F. Ehlers . I do not know, which combination works best, so you can experiment.
If no Adaptation is selected ( None option), you can set Length directly. If an Adaptation is selected, then Cycle multiplier can be set.
The oscillator also has the option to configure the internal smoothing function with Window setting. By default, RMA is used (like in ADX calculation). Fast Default option is using half the length for smoothing. Triangle , Hamming and Hann Window algorithms are some better smoothers suggested by John F. Ehlers.
After the oscillator a Moving Average can be applied. The following Moving Averages are included: SMA , RMA, EMA , HMA , VWMA , 2-pole Super Smoother, 3-pole Super Smoother, Filt11, Triangle Window, Hamming Window, Hann Window, Lowpass, DSSS.
Postfilter options are applied last:
Stochastic - Stochastic
Super Smooth Stochastic - Super Smooth Stochastic (part of MESA Stochastic ) by John F. Ehlers
Inverse Fisher Transform - Inverse Fisher Transform
Noise Elimination Technology - a simplified Kendall correlation algorithm "Noise Elimination Technology" by John F. Ehlers
Momentum - momentum (derivative)
Except for Inverse Fisher Transform , all Postfilter algorithms can have Length parameter. If it is not specified (set to 0), then the calculated Slow MA Length is used. If Filter/MA Length is less than 2 or Postfilter Length is less than 1, they are calculated as a multiplier of the calculated oscillator length.
More information on the algorithms is given in the code for the libraries used. I am also very grateful to other TradingView community members (they are also mentioned in the library code) without whom this script would not have been possible.
Forex Pips Tracker PinescriptlabsThis algorithm is exclusively designed for the Forex market 🌐 and serves as a tool to measure volatility, helping to determine on average how many pips positions move per hour. With this information, a trader can place take profit and stop loss orders with greater certainty, since they know the average pip movement range during each hour of the day.
What does it do and how does it work?
• Volatility measurement in pips 📊:
The algorithm calculates the size of the movement (or range) of each candle expressed in pips. To do this, it takes the difference between the highest and lowest price of each candle and converts it into pips.
👉
• Time zone adjustment ⏰:
It allows you to configure the time zone so that the data aligns with your desired schedule. This is especially useful for comparing movements at different times based on the trader's location.
• Analysis by time intervals 🕒:
The algorithm’s logic organizes the information for each hour of the day. It stores data for the current day, the previous day, weekly, and historically (200 candles). This allows you to see how volatility varies across different periods, providing a dynamic view of market behavior.
👉
• Directionality of movement 🔄:
In addition to averaging the pip range, the algorithm determines the predominant direction of each candle (bullish or bearish). This translates into visual indicators (like arrows) that help identify whether, on average, the movement during that hour tends to go up or down.
• Table visualization 📈:
Finally, the information is presented in an integrated table on the chart. Each row corresponds to an hour of the day and shows the average number of pips and the direction (bullish, bearish, or neutral) for each analyzed period. This table makes it easy to quickly and practically interpret the volatility data.
By combining these features, the algorithm becomes an essential tool for traders looking to better understand market dynamics and optimize their trading strategies! 💼✨
Español:
Este algoritmo está diseñado exclusivamente para el mercado Forex 🌐 y sirve como una herramienta para medir la volatilidad, ayudando a determinar en promedio cuántos pips se mueven las posiciones por hora. Con esta información, un trader puede colocar el take profit y el stop loss con mayor certeza, ya que conoce el rango promedio de movimiento en pips durante cada hora del día.
¿Qué hace y cómo funciona?
• Medición de volatilidad en pips 📊:
El algoritmo calcula el tamaño del movimiento (o rango) de cada vela expresado en pips. Para ello, toma la diferencia entre el precio máximo y el mínimo de cada vela y la convierte a pips.
👉
• Ajuste de zona horaria ⏰:
Permite configurar la zona horaria para que los datos se ajusten al horario deseado. Esto es especialmente útil para comparar movimientos durante distintas horas en función de la localización del trader.
• Análisis por intervalos de tiempo 🕒:
La lógica del algoritmo organiza la información por cada hora del día. Guarda datos para el día actual, el día anterior, a nivel semanal e histórico (200 velas). Esto permite ver cómo varía la volatilidad en diferentes periodos, proporcionando una visión dinámica del comportamiento del mercado.
👉
• Direccionalidad del movimiento 🔄:
Además de promediar el rango en pips, el algoritmo determina la dirección predominante de cada vela (alcista o bajista). Esto se traduce en indicadores visuales (como flechas) que permiten identificar si, en promedio, el movimiento en esa hora tiende a subir o bajar.
• Visualización en tabla 📈:
Finalmente, la información se presenta en una tabla integrada en el gráfico. Cada fila corresponde a una hora del día y muestra el promedio de pips y la dirección (alcista, bajista o neutral) para cada uno de los periodos analizados. Esta tabla facilita la interpretación rápida y práctica de los datos de volatilidad.
Al combinar estas funciones, el algoritmo se convierte en una herramienta esencial para traders que buscan entender mejor la dinámica del mercado y optimizar sus estrategias de trading! 💼✨
Dual Zigzag [Trendoscope®]🎲 Dual Zigzag indicator is built on recursive zigzag algorithm. It is very similar to other zigzag indicators published by us and other authors. However, the key point here is, the indicator draws zigzag on both price and any other plot based indicator on separate layouts.
Before we get into the indicator, here are some brief descriptions of the underlying concepts and key terminologies
🎯 Zigzag
Zigzag indicator breaks down price or any input series into a series of Pivot Highs and Pivot Lows alternating between each other. Zigzags though shows pivot high and lows, should not be used for buying at low and selling at high. The main application of zigzag indicator is for the visualisation of market structure and this can be used as basic building block for any pattern recognition algorithms.
🎯 Recursive Zigzag Algorithm
Recursive zigzag algorithm builds zigzag on multiple levels and each level of zigzag is based on the previous level pivots. The level zero zigzag is built on price. However, for level 1, instead of price level 0 zigzag pivots are used. Similarly for level 2, level 1 zigzag pivots are used as base.
🎲 Components Dual Zigzag Indicator
Here are the components of Dual zigzag indicator
Built in Oscillator - Indicator has built in oscillator options for plotting RSI (Relative Strength Index), MFI (Money Flow Index), cci (Commodity Channel Index) , CMO (Chande Momentum Oscillator), COG (Center of Gravity), and ROC (Rate of Change). Apart from the given built in oscillators, users can also use a custom external output as base. The oscillators are not printed on the price pane. But, printed on a separate indicator overlay.
Zigzag On Oscillator - Recursive zigzag is calculated and printed on the oscillator series. Each pivot high and pivot low also prints a label having the retracement ratios, and price levels at those points. Zigzag on the oscillator is also printed on the indicator overlay pane.
Zigzag on Price - Recursive zigzag calculated based on price and printed on the price pane. This is made possible by using force_overlay option present in the drawing objects. At each zigzag pivot levels, the label having price retracement ratios, and oscillator values are printed.
It is called dual zigzag because, the indicator calculates the zigzag on both price and oscillator series of values and prints them separately on different panes on the chart.
🎲 Indicator Settings
Settings include
Theme display settings to get the right colour combination to match the background.
Zigzag settings to be used for zigzag calculation and display
Oscillator settings to chose the oscillator to be used as base for 2nd zigzag
🎲 Applications
Useful in spotting divergences with both indicator and price having their own zigzag to highlight pivots
Spotting patterns in indicators/oscillators and correlate them with the patterns on price
🎲 Using External Input
If users want to use an external indicator such as OBV instead of the built in oscillators, then can do so by using the custom option.
Here is how this can be done.
Step1. Add both Dual Zigzag and the intended indicator (in this case OBV) on the chart. Notice that both OBV and Dual zigzag appear on different panes.
Step2. Edit the indicator settings of Dual zigzag and set custom indicator by selecting "custom" as oscillator name and then by setting the custom external indicator name and input.
Step 3. You would notice that the zigzag in Dual Zigzag indictor pane is already showing the zigzag pivots based on the OBV indicator and the price pivots display obv values at the pivot points. We can leave this as is.
Step 4. As an additional step, you can also merge the OBV pane and the Dual zigzag indicator pane into one by going into OBV settings and moving the indicator to above pane. Merge the scales so that there is no two scales on the same pane and the entire scale appear on the right.
At the end, you should see two panes - one with price and other with OBV and both having their zigzag plotted.
Endpointed SSA of Price [Loxx]The Endpointed SSA of Price: A Comprehensive Tool for Market Analysis and Decision-Making
The financial markets present sophisticated challenges for traders and investors as they navigate the complexities of market behavior. To effectively interpret and capitalize on these complexities, it is crucial to employ powerful analytical tools that can reveal hidden patterns and trends. One such tool is the Endpointed SSA of Price, which combines the strengths of Caterpillar Singular Spectrum Analysis, a sophisticated time series decomposition method, with insights from the fields of economics, artificial intelligence, and machine learning.
The Endpointed SSA of Price has its roots in the interdisciplinary fusion of mathematical techniques, economic understanding, and advancements in artificial intelligence. This unique combination allows for a versatile and reliable tool that can aid traders and investors in making informed decisions based on comprehensive market analysis.
The Endpointed SSA of Price is not only valuable for experienced traders but also serves as a useful resource for those new to the financial markets. By providing a deeper understanding of market forces, this innovative indicator equips users with the knowledge and confidence to better assess risks and opportunities in their financial pursuits.
█ Exploring Caterpillar SSA: Applications in AI, Machine Learning, and Finance
Caterpillar SSA (Singular Spectrum Analysis) is a non-parametric method for time series analysis and signal processing. It is based on a combination of principles from classical time series analysis, multivariate statistics, and the theory of random processes. The method was initially developed in the early 1990s by a group of Russian mathematicians, including Golyandina, Nekrutkin, and Zhigljavsky.
Background Information:
SSA is an advanced technique for decomposing time series data into a sum of interpretable components, such as trend, seasonality, and noise. This decomposition allows for a better understanding of the underlying structure of the data and facilitates forecasting, smoothing, and anomaly detection. Caterpillar SSA is a particular implementation of SSA that has proven to be computationally efficient and effective for handling large datasets.
Uses in AI and Machine Learning:
In recent years, Caterpillar SSA has found applications in various fields of artificial intelligence (AI) and machine learning. Some of these applications include:
1. Feature extraction: Caterpillar SSA can be used to extract meaningful features from time series data, which can then serve as inputs for machine learning models. These features can help improve the performance of various models, such as regression, classification, and clustering algorithms.
2. Dimensionality reduction: Caterpillar SSA can be employed as a dimensionality reduction technique, similar to Principal Component Analysis (PCA). It helps identify the most significant components of a high-dimensional dataset, reducing the computational complexity and mitigating the "curse of dimensionality" in machine learning tasks.
3. Anomaly detection: The decomposition of a time series into interpretable components through Caterpillar SSA can help in identifying unusual patterns or outliers in the data. Machine learning models trained on these decomposed components can detect anomalies more effectively, as the noise component is separated from the signal.
4. Forecasting: Caterpillar SSA has been used in combination with machine learning techniques, such as neural networks, to improve forecasting accuracy. By decomposing a time series into its underlying components, machine learning models can better capture the trends and seasonality in the data, resulting in more accurate predictions.
Application in Financial Markets and Economics:
Caterpillar SSA has been employed in various domains within financial markets and economics. Some notable applications include:
1. Stock price analysis: Caterpillar SSA can be used to analyze and forecast stock prices by decomposing them into trend, seasonal, and noise components. This decomposition can help traders and investors better understand market dynamics, detect potential turning points, and make more informed decisions.
2. Economic indicators: Caterpillar SSA has been used to analyze and forecast economic indicators, such as GDP, inflation, and unemployment rates. By decomposing these time series, researchers can better understand the underlying factors driving economic fluctuations and develop more accurate forecasting models.
3. Portfolio optimization: By applying Caterpillar SSA to financial time series data, portfolio managers can better understand the relationships between different assets and make more informed decisions regarding asset allocation and risk management.
Application in the Indicator:
In the given indicator, Caterpillar SSA is applied to a financial time series (price data) to smooth the series and detect significant trends or turning points. The method is used to decompose the price data into a set number of components, which are then combined to generate a smoothed signal. This signal can help traders and investors identify potential entry and exit points for their trades.
The indicator applies the Caterpillar SSA method by first constructing the trajectory matrix using the price data, then computing the singular value decomposition (SVD) of the matrix, and finally reconstructing the time series using a selected number of components. The reconstructed series serves as a smoothed version of the original price data, highlighting significant trends and turning points. The indicator can be customized by adjusting the lag, number of computations, and number of components used in the reconstruction process. By fine-tuning these parameters, traders and investors can optimize the indicator to better match their specific trading style and risk tolerance.
Caterpillar SSA is versatile and can be applied to various types of financial instruments, such as stocks, bonds, commodities, and currencies. It can also be combined with other technical analysis tools or indicators to create a comprehensive trading system. For example, a trader might use Caterpillar SSA to identify the primary trend in a market and then employ additional indicators, such as moving averages or RSI, to confirm the trend and generate trading signals.
In summary, Caterpillar SSA is a powerful time series analysis technique that has found applications in AI and machine learning, as well as financial markets and economics. By decomposing a time series into interpretable components, Caterpillar SSA enables better understanding of the underlying structure of the data, facilitating forecasting, smoothing, and anomaly detection. In the context of financial trading, the technique is used to analyze price data, detect significant trends or turning points, and inform trading decisions.
█ Input Parameters
This indicator takes several inputs that affect its signal output. These inputs can be classified into three categories: Basic Settings, UI Options, and Computation Parameters.
Source: This input represents the source of price data, which is typically the closing price of an asset. The user can select other price data, such as opening price, high price, or low price. The selected price data is then utilized in the Caterpillar SSA calculation process.
Lag: The lag input determines the window size used for the time series decomposition. A higher lag value implies that the SSA algorithm will consider a longer range of historical data when extracting the underlying trend and components. This parameter is crucial, as it directly impacts the resulting smoothed series and the quality of extracted components.
Number of Computations: This input, denoted as 'ncomp,' specifies the number of eigencomponents to be considered in the reconstruction of the time series. A smaller value results in a smoother output signal, while a higher value retains more details in the series, potentially capturing short-term fluctuations.
SSA Period Normalization: This input is used to normalize the SSA period, which adjusts the significance of each eigencomponent to the overall signal. It helps in making the algorithm adaptive to different timeframes and market conditions.
Number of Bars: This input specifies the number of bars to be processed by the algorithm. It controls the range of data used for calculations and directly affects the computation time and the output signal.
Number of Bars to Render: This input sets the number of bars to be plotted on the chart. A higher value slows down the computation but provides a more comprehensive view of the indicator's performance over a longer period. This value controls how far back the indicator is rendered.
Color bars: This boolean input determines whether the bars should be colored according to the signal's direction. If set to true, the bars are colored using the defined colors, which visually indicate the trend direction.
Show signals: This boolean input controls the display of buy and sell signals on the chart. If set to true, the indicator plots shapes (triangles) to represent long and short trade signals.
Static Computation Parameters:
The indicator also includes several internal parameters that affect the Caterpillar SSA algorithm, such as Maxncomp, MaxLag, and MaxArrayLength. These parameters set the maximum allowed values for the number of computations, the lag, and the array length, ensuring that the calculations remain within reasonable limits and do not consume excessive computational resources.
█ A Note on Endpionted, Non-repainting Indicators
An endpointed indicator is one that does not recalculate or repaint its past values based on new incoming data. In other words, the indicator's previous signals remain the same even as new price data is added. This is an important feature because it ensures that the signals generated by the indicator are reliable and accurate, even after the fact.
When an indicator is non-repainting or endpointed, it means that the trader can have confidence in the signals being generated, knowing that they will not change as new data comes in. This allows traders to make informed decisions based on historical signals, without the fear of the signals being invalidated in the future.
In the case of the Endpointed SSA of Price, this non-repainting property is particularly valuable because it allows traders to identify trend changes and reversals with a high degree of accuracy, which can be used to inform trading decisions. This can be especially important in volatile markets where quick decisions need to be made.
LengthAdaptationCollection of dynamic length adaptation algorithms. Mostly from various Adaptive Moving Averages (they are usually just EMA otherwise). Now you can combine Adaptations with any other Moving Averages or Oscillators (see my other libraries), to get something like Deviation Scaled RSI or Fractal Adaptive VWMA. This collection is not encyclopaedic. Suggestions are welcome.
chande(src, len, sdlen, smooth, power) Chande's Dynamic Length
Parameters:
src : Series to use
len : Reference lookback length
sdlen : Lookback length of Standard deviation
smooth : Smoothing length of Standard deviation
power : Exponent of the length adaptation (lower is smaller variation)
Returns: Calculated period
Taken from Chande's Dynamic Momentum Index (CDMI or DYMOI), which is dynamic RSI with this length
Original default power value is 1, but I use 0.5
A variant of this algorithm is also included, where volume is used instead of price
vidya(src, len, dynLow) Variable Index Dynamic Average Indicator (VIDYA)
Parameters:
src : Series to use
len : Reference lookback length
dynLow : Lower bound for the dynamic length
Returns: Calculated period
Standard VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
I took the adaptation part, as it is just an EMA otherwise
vidyaRS(src, len, dynHigh) Relative Strength Dynamic Length - VIDYA RS
Parameters:
src : Series to use
len : Reference lookback length
dynHigh : Upper bound for the dynamic length
Returns: Calculated period
Based on Vitali Apirine's modification (Stocks and Commodities, January 2022) of VIDYA algorithm. The period oscillates from the Upper Bound down (fast)
I took the adaptation part, as it is just an EMA otherwise
kaufman(src, len, dynLow, dynHigh) Kaufman Efficiency Scaling
Parameters:
src : Series to use
len : Reference lookback length
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
Returns: Calculated period
Based on Efficiency Ratio calculation orifinally used in Kaufman Adaptive Moving Average developed by Perry J. Kaufman
I took the adaptation part, as it is just an EMA otherwise
ds(src, len) Deviation Scaling
Parameters:
src : Series to use
len : Reference lookback length
Returns: Calculated period
Based on Derivation Scaled Super Smoother (DSSS) by John F. Ehlers
Originally used with Super Smoother
RMS originally has 50 bar lookback. Changed to 4x length for better flexibility. Could be wrong.
maa(src, len, threshold) Median Average Adaptation
Parameters:
src : Series to use
len : Reference lookback length
threshold : Adjustment threshold (lower is smaller length, default: 0.002, min: 0.0001)
Returns: Calculated period
Based on Median Average Adaptive Filter by John F. Ehlers
Discovered and implemented by @cheatcountry:
I took the adaptation part, as it is just an EMA otherwise
fra(len, fc, sc) Fractal Adaptation
Parameters:
len : Reference lookback length
fc : Fast constant (default: 1)
sc : Slow constant (default: 200)
Returns: Calculated period
Based on FRAMA by John F. Ehlers
Modified to allow lower and upper bounds by an unknown author
I took the adaptation part, as it is just an EMA otherwise
mama(src, dynLow, dynHigh) MESA Adaptation - MAMA Alpha
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
Returns: Calculated period
Based on MESA Adaptive Moving Average by John F. Ehlers
Introduced in the September 2001 issue of Stocks and Commodities
Inspired by the @everget implementation:
I took the adaptation part, as it is just an EMA otherwise
doAdapt(type, src, len, dynLow, dynHigh, chandeSDLen, chandeSmooth, chandePower) Execute a particular Length Adaptation from the list
Parameters:
type : Length Adaptation type to use
src : Series to use
len : Reference lookback length
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
chandeSDLen : Lookback length of Standard deviation for Chande's Dynamic Length
chandeSmooth : Smoothing length of Standard deviation for Chande's Dynamic Length
chandePower : Exponent of the length adaptation for Chande's Dynamic Length (lower is smaller variation)
Returns: Calculated period (float, not limited)
doMA(type, src, len) MA wrapper on wrapper: if DSSS is selected, calculate it here
Parameters:
type : MA type to use
src : Series to use
len : Filtering length
Returns: Filtered series
Demonstration of a combined indicator: Deviation Scaled Super Smoother
DMI + HMA - No Risk ManagementDMI (Directional Movement Index) and HMA (Hull Moving Average)
The DMI and HMA make a great combination, The DMI will gauge the market direction, while the HMA will add confirmation to the trend strength.
What is the DMI?
The DMI is an indicator that was developed by J. Welles Wilder in 1978. The Indicator was designed to identify in which direction the price is moving. This is done by comparing previous highs and lows and drawing 2 lines.
1. A Positive movement line
2. A Negative movement line
A third line can be added, which would be known as the ADX line or Average Directional Index. This can also be used to gauge the strength in which direction the market is moving.
When the Positive movement line (DI+) is above the Negative movement line (DI-) there is more upward pressure. Ofcourse visa versa, when the DI- is above the DI+ that would indicate more downwards pressure.
Want to know more about HMA? Check out one of our other published scripts
What is this strategy doing?
We are first waiting for the DMI to cross in our favoured direction, after that, we wait for the HMA to signal the entry. Without both conditions being true, no trade will be made.
Long Entries
1. DI+ crosses above DI-
2. HMA line 1 is above HMA line 2
Short Entries
1. DI- Crosses above DI+
2. HMA line 1 is below HMA lilne 2
Its as simple as that.
Conclusion
While this strategy does have its downsides, that can be reduced by adding some risk manegment into the script. In general the trade profitability is above average, And the max drawdown is at a minimum.
The settings have been optimised to suite BTCUSDT PERP markets. Though with small adjustments it can be used on many assets!
SMU Stock ThermometerThis script shows various technical indicators in a stacked vertical candle called Market Termometer.
It helps to see the price action in one single vertical column where the actual price moves up or down. So you can see the price change based on your custom setting levels.
I've been studying ALGO for over a year and made many live experiment trades long and shorts. So, I'm trying to find a way to see what is ALGos next move. If it sounds far-fetch, then you should see my other published scripts.
Here is example of how ALGo dance around old indicators, which is why I started creating a bunch of new indicators that ALGO doesn't know
Example:
Impact-driven-algorithm= Large volume masked as small volume to keep the price at desired level. So, your chart says overbought but market doesn't drop for days
Cost-driven-algorithm= Hedge fund buy every time at lower price and prevent others to buy low, moving up fast. Is like a clock with millisecond timing and ALGO owners know when to buy low and when to sell high
If you have a good idea, let me know so i can include it the future versions.
Enjoy and think outside the box, the only way to beat the ALGO
3D Surface Modeling [PhenLabs]📊 3D Surface Modeling
Version: PineScript™ v6
📌 Description
The 3D Surface Modeling indicator revolutionizes technical analysis by generating three-dimensional visualizations of multiple technical indicators across various timeframes. This advanced analytical tool processes and renders complex indicator data through a sophisticated matrix-based calculation system, creating an intuitive 3D surface representation of market dynamics.
The indicator employs array-based computations to simultaneously analyze multiple instances of selected technical indicators, mapping their behavior patterns across different temporal dimensions. This unique approach enables traders to identify complex market patterns and relationships that may be invisible in traditional 2D charts.
🚀 Points of Innovation
Matrix-Based Computation Engine: Processes up to 500 concurrent indicator calculations in real-time
Dynamic 3D Rendering System: Creates depth perception through sophisticated line arrays and color gradients
Multi-Indicator Integration: Seamlessly combines VWAP, Hurst, RSI, Stochastic, CCI, MFI, and Fractal Dimension analyses
Adaptive Scaling Algorithm: Automatically adjusts visualization parameters based on indicator type and market conditions
🔧 Core Components
Indicator Processing Module: Handles real-time calculation of multiple technical indicators using array-based mathematics
3D Visualization Engine: Converts indicator data into three-dimensional surfaces using line arrays and color mapping
Dynamic Scaling System: Implements custom normalization algorithms for different indicator types
Color Gradient Generator: Creates depth perception through programmatic color transitions
🔥 Key Features
Multi-Indicator Support: Comprehensive analysis across seven different technical indicators
Customizable Visualization: User-defined color schemes and line width parameters
Real-time Processing: Continuous calculation and rendering of 3D surfaces
Cross-Timeframe Analysis: Simultaneous visualization of indicator behavior across multiple periods
🎨 Visualization
Surface Plot: Three-dimensional representation using up to 500 lines with dynamic color gradients
Depth Indicators: Color intensity variations showing indicator value magnitude
Pattern Recognition: Visual identification of market structures across multiple timeframes
📖 Usage Guidelines
Indicator Selection
Type: VWAP, Hurst, RSI, Stochastic, CCI, MFI, Fractal Dimension
Default: VWAP
Starting Length: Minimum 5 periods
Default: 10
Step Size: Interval between calculations
Range: 1-10
Visualization Parameters
Color Scheme: Green, Red, Blue options
Line Width: 1-5 pixels
Surface Resolution: Up to 500 lines
✅ Best Use Cases
Multi-timeframe market analysis
Pattern recognition across different technical indicators
Trend strength assessment through 3D visualization
Market behavior study across multiple periods
⚠️ Limitations
High computational resource requirements
Maximum 500 line restriction
Requires substantial historical data
Complex visualization learning curve
🔬 How It Works
1. Data Processing:
Calculates selected indicator values across multiple timeframes
Stores results in multi-dimensional arrays
Applies custom scaling algorithms
2. Visualization Generation:
Creates line arrays for 3D surface representation
Applies color gradients based on value magnitude
Renders real-time updates to surface plot
3. Display Integration:
Synchronizes with chart timeframe
Updates surface plot dynamically
Maintains visual consistency across updates
🌟 Credits:
Inspired by LonesomeTheBlue (modified for multiple indicator types with scaling fixes and additional unique mappings)
💡 Note:
Optimal performance requires sufficient computing resources and historical data. Users should start with default settings and gradually adjust parameters based on their analysis requirements and system capabilities.
