[blackcat] L2 Ehlers Autocorrelation Periodogram V2OVERVIEW
The Ehlers Autocorrelation Periodogram is a sophisticated technical analysis tool that identifies market cycles and their dominant frequencies using autocorrelation and spectral analysis techniques.
BACKGROUND
Developed by John F. Ehlers and detailed in his book "Cycle Analytics for Traders" (2013), this indicator combines autocorrelation functions with discrete Fourier transforms to extract cyclic information from price data.
FUNCTION
The indicator works through these key steps:
Calculates autocorrelation using minimum three-bar averaging
Applies discrete Fourier transform to extract cyclic information
Uses center-of-gravity algorithm to determine dominant cycle
ADVANTAGES
• Rapid response within half-cycle periods
• Accurate relative cyclic power estimation over time
• Correlation constraints between -1 and +1 eliminate amplitude compensation needs
• High resolution independent of windowing functions
HOW TO USE
Add the indicator to your chart
Adjust AvgLength input parameter:
• Default: 3 bars
• Higher values increase smoothing
• Lower values increase sensitivity
Interpret the results:
• Colored bars represent spectral power
• Red to yellow spectrum indicates cycle strength
• White line shows dominant cycle period
INTERPRETATION
• Strong colors indicate significant cyclic activity
• Sharp color transitions suggest potential cycle changes
• Dominant cycle line helps identify primary market rhythm
LIMITATIONS
• Requires sufficient historical data
• Performance may vary in non-cyclical markets
• Results depend on proper parameter settings
NOTES
• Uses highpass and super smoother filtering techniques
• Spectral estimates are normalized between 0 and 1
• Color intensity varies based on spectral power
THANKS
This implementation is based on Ehlers' original work and has been adapted for TradingView's Pine Script platform.
Komut dosyalarını "Cycle" için ara
SW Gann DaysGann pressure days, named after the famous trader W.D. Gann, refer to specific days in a trading month that are believed to have significant market influence. These days are identified based on Gann's theories of astrology, geometry, and market cycles. Here’s a general outline of how they might be understood:
1. **Market Cycles**: Gann believed that markets move in cycles and that certain days can have heightened volatility or trend changes. Traders look for specific dates based on historical price movements.
2. **Timing Indicators**: Pressure days often align with key economic reports, earnings announcements, or geopolitical events that can cause price swings.
3. **Mathematical Patterns**: Gann used angles and geometric patterns to predict price movements, with pressure days potentially aligning with these calculations.
4. **Historical Patterns**: Traders analyze past data to identify dates that historically show strong price reactions, using this to predict future behavior.
5. **Astrological Influences**: Some practitioners incorporate astrological elements, believing that celestial events (like full moons or planetary alignments) can impact market psychology.
Traders might use these concepts to make decisions about entering or exiting positions, but it’s important to note that Gann's methods can be complex and are not universally accepted in trading communities.
Retrograde Periods (Multi-Planet)**Retrograde Periods (Multi-Planet) Indicator**
This TradingView script overlays your chart with a dynamic visualization of planetary retrograde periods. Built in Pine Script v6, it computes and displays the retrograde status of eight planets—Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto—using hard-coded retrograde intervals from 2009 to 2026.
**Key Features:**
- Dynamic Background Coloring:
The indicator changes the chart’s background color based on the current retrograde status of the planets. The colors follow a priority order (Mercury > Venus > Mars > Jupiter > Saturn > Uranus > Neptune > Pluto) so that if multiple planets are retrograde simultaneously, the highest-priority planet’s color is displayed.
- Interactive Planet Selection:
User-friendly checkboxes allow you to choose which planets to list in the table’s “Selected” row. Note that while these checkboxes control the display of the planet names in the table, the retrograde calculations remain independent of these selections.
- Real-Time Retrograde Status Table:
A table in the top-right corner displays each planet’s retrograde status in real time. “Yes” is shown in red for a planet in retrograde and “No” in green when it isn’t. This offers an at-a-glance view of the cosmic conditions influencing your charts.
- Astrological & Astronomical Insights:
Whether you’re into sidereal astrology or simply fascinated by celestial mechanics, this script lets you visualize those retrograde cycles. In astrology, retrograde periods are often seen as times for reflection and re-evaluation, while in astronomy they reflect the natural orbital motions seen from our perspective on Earth.
Enhance your trading setup by integrating cosmic cycles into your technical analysis. Happy trading and cosmic exploring!
Gann & Fibonacci Analysis for MSTRYes! Below is a step-by-step guide to performing Gann Analysis on MSTR in TradingView for the last year.
Step 1: Set Up the Chart
Open TradingView and search for MSTR (MicroStrategy).
Select the 1-day (D) timeframe to analyze the past year.
Set your chart to logarithmic scale (⚙ Settings → Scale → Log).
Enable grid lines for alignment (⚙ Settings → Appearance → Grid Lines).
Step 2: Identify Key Highs and Lows (Last Year)
Find the 52-week high and 52-week low for MSTR.
As of now:
52-Week High: ~$999 (March 2024).
52-Week Low: ~$280 (October 2023).
Step 3: Plot Gann Angles
Using TradingView's Gann Fan Tool:
Select "Gann Fan" (Press / and type “Gann Fan” to find it).
Start at the 52-week low (~$280, October 2023) and drag upwards.
Adjust the angles to match key levels:
1x1 (45°) → Main trendline
2x1 (26.5°) → Strong uptrend
4x1 (15°) → Weak trendline
1x2 (63.75°) → Strong resistance
Repeat the process from the 52-week high (~$999, March 2024) downward to see bearish angles.
Step 4: Apply Fibonacci & Gann Retracement Levels
Using Fibonacci Retracement:
Select "Fibonacci Retracement" tool.
Draw from 52-week high ($999) to 52-week low ($280).
Enable key Fibonacci levels:
23.6% ($816)
38.2% ($678)
50% ($640)
61.8% ($550)
78.6% ($430)
Watch for price reactions near these levels.
Using Gann Retracement Levels:
Select "Gann Box" in TradingView.
Draw from 52-week high ($999) to low ($280).
Enable key Gann retracement levels:
12.5% ($912)
25% ($850)
37.5% ($768)
50% ($640)
62.5% ($550)
75% ($480)
87.5% ($350)
Identify confluences with Gann angles and Fibonacci levels.
Step 5: Identify Significant Dates & Time Cycles
Use "Date Range" Tool in TradingView.
Mark major turning points:
High → Low: ~180 days (Half-year cycle).
Low → High: ~90 days (Quarter cycle).
Use Square-Outs (Time = Price method):
Example: If MSTR hit $500, check 500 days from key events.
Mark key anniversaries of past highs/lows for possible reversals.
Step 6: Analyze and Trade Execution
✅ If MSTR is at a Gann angle + Fibonacci level + key date → Expect a reaction.
✅ Use RSI, MACD, and Volume for extra confirmation.
✅ Set Stop-Loss at nearest Gann support/resistance.
Dominant Direction (DD)The Dominant Direction indicator is a custom technical analysis tool that uses the Dominant Cycle Estimators library to identify the dominant trend direction in the market. The indicator utilizes the MAMA Cycle function, which is a part of the library, to calculate the period of the data. The resulting period is then used to plot lines on the chart that represent the dominant trend direction.
The indicator takes two inputs, the source of data, and the high and low values of the source. The MAMA Cycle function is used to calculate the period of the data, with the lower bound and upper bound of the dynamic length defined by the user. The indicator then plots lines on the chart to represent the dominant trend direction. The lines are plotted from the current bar to the bar that is a certain number of periods away, as defined by the MAMA Cycle function, in the direction of the trend.
The indicator also has a feature of removing the lines when the trend is no longer confirmed. If the bar state is confirmed, the line is deleted and this helps the user to have a clearer view of the chart.
In summary, the Dominant Direction indicator is a powerful tool for identifying the dominant trend direction in the market. It uses the MAMA Cycle function to calculate the period of the data and plots lines on the chart to represent the dominant trend direction. This can help traders identify potential entry and exit points, and make more informed trading decisions.
True Open CalculationsIndicator Description: True Open Calculations
This custom Pine Script indicator calculates and plots key "True Open" levels based on specific time intervals and trading sessions. The True Open levels represent significant price points on the chart, helping traders identify key reference points tied to various market opening times. These levels are important for understanding price action in relation to market sessions and trading cycles. The indicator is designed to plot lines corresponding to different "True Opens" on the chart and display labels with the associated information.
Key Features:
True Year Open:
This represents the opening price on the first Monday of April each year. It serves as a reference point for the yearly price level.
Plot Color: Green.
True Month Open:
This represents the opening price on the second Monday of each month. It helps in identifying monthly trends and provides a key reference for monthly price movements.
Plot Color: Blue.
True Week Open:
This represents the opening price every Monday at 6:00 PM. It gives traders a level to track weekly opening movements and can be useful for weekly trend analysis.
Plot Color: Orange.
True Day Open:
This represents the opening price at 12:00 AM (midnight) each day. It serves as a daily benchmark for price action at the start of the trading day.
Plot Color: Red.
True New York Session Open:
This represents the opening price at 7:30 AM (New York session start time). This level is crucial for traders focused on the New York trading session.
Plot Color: Purple.
Additional Features:
Labels: The indicator displays labels to the right of each plotted line to describe which "True Open" it represents (e.g., "True Year Open," "True Month Open," etc.).
Dynamic Plotting: The lines are only plotted on the current candle, and the lines are dynamically updated for each time period based on the corresponding "True Open."
Visual Cues: The colors of the plotted lines (green, blue, orange, red, purple) help quickly distinguish between different "True Open" levels, making it easy for traders to track price action and make informed decisions.
Use Cases:
Yearly, Monthly, Weekly, Daily, and Session Benchmarking: This indicator provides traders with important price levels to use as benchmarks for the current year, month, week, and day, helping to identify trends and potential reversals.
Session Awareness: It is particularly useful for traders who want to track key market sessions, such as the New York session, and their impact on price movement.
Long-term Analysis: By including the yearly open, this indicator helps traders gain a broader perspective on market trends and provides context for analyzing shorter-term price movements.
Benefits:
Helps identify important reference points for longer-term trends (yearly, monthly) as well as shorter-term moves (daily, weekly, and session).
Visually intuitive with color-coded lines and labels, allowing quick and easy identification of key market open levels.
Dynamic and real-time: The indicator plots and updates the True Open levels dynamically as the market progresses.
Trading Sessions Highs/Lows | InvrsROBINHOODTrading Sessions Highs/Lows | InvrsROBINHOOD
🚀 A powerful indicator for tracking key trading sessions and the highs and lows of each session!
📌 Description
The Trading Sessions Highs/Lows indicator visually marks the most critical trading sessions—Asia, London, and New York—using small colored dots at the bottom of the candle. It also tracks and plots the highs and lows of each session, along with the Daily Open and Weekly Open levels.
This tool is designed to help traders identify session-based liquidity zones, price reactions, and potential trade setups with minimal chart clutter.
Key Features:
✅ Session markers (Asia, London, NY AM, NY Lunch, NY PM) plotted as small dots
✅ Plots session highs and lows for market structure insights
✅ Daily Open line for intraday reference
✅ Weekly Open line for higher timeframe bias
✅ Alerts for session high/low breaks to capture momentum shifts
✅ User-defined UTC offset for global traders
✅ Customizable session colors for personal preference
📖 How to Use the Indicator
1️⃣ Understanding the Sessions
Asia Session (Yellow Dot) → Marks liquidity buildup & pre-London moves
London Session (Blue Dot) → Strong volatility, breakout opportunities
New York AM Session (Green Dot) → Major trends & institutional participation
New York Lunch (Red Dot) → Low volume, ranging market
New York PM Session (Dark Green Dot) → End-of-day movements & reversals
2️⃣ Session Highs & Lows for Market Structure
Session Highs can act as resistance or breakout points.
Session Lows can act as support or stop-hunt zones.
Break of a session high/low with volume may indicate continuation or reversal.
3️⃣ Using the Daily & Weekly Open
The Daily Open (Black Line) helps gauge the intraday trend.
Above Daily Open → Bearish Bias
Below Daily Open → Bullish Bias
The Weekly Open (Red Line) sets the higher timeframe directional bias.
4️⃣ Alerts for Breakouts
The indicator will trigger alerts when price breaks session highs or lows.
Useful for setting stop-losses, breakout trades, and risk management.
💡 Why This Indicator is Important for Beginners
1️⃣ Avoids Overtrading:
Many beginners trade in low-volume periods (NY Lunch, Asia session) and get stuck in choppy price action.
This indicator highlights when volatility is high so traders focus on better opportunities.
2️⃣ Session-Based Liquidity Traps:
Market makers often run stops at session highs/lows before reversing.
Watching session breaks prevents traders from falling into liquidity grabs.
3️⃣ Reduces Emotional Trading:
If price is above the Daily Open, a beginner shouldn’t look for shorts.
If price is below a key session low, it may signal a fake breakout.
4️⃣ Aligns with Institutional Trading:
Smart money traders use session highs/lows to set stop hunts & reversals.
Beginners can use this indicator to spot these zones before entering trades.
🛡️ How to Mitigate Risk with This Indicator
✅ Wait for Confirmations – Don’t trade blindly at session highs/lows. Look for wicks, rejections, or break/retests.
✅ Use Stop-Loss Above/Below Session Levels – If you’re going long, set SL below a session low. If short, set SL above a session high.
✅ Watch Volume & News Events – Breakouts without strong volume or news may be fake moves.
✅ Combine with Other Strategies – Use price action, trendlines, or EMAs with this indicator for higher probability trades.
✅ Use the Weekly Open for Trend Bias – If price stays below the Weekly Open, avoid bullish setups unless key support holds.
🎯 Who is This Indicator For?
📌 Beginners who need clear session-based trading levels.
📌 Day traders & scalpers looking to refine their intraday setups.
📌 Smart money traders using liquidity concepts.
📌 Swing traders tracking higher timeframe momentum shifts.
🚀 Final Thoughts
This indicator is an essential tool for traders who want to understand market structure, liquidity, and volatility cycles. Whether you’re trading forex, stocks, or crypto, it helps you stay on the right side of the market and avoid unnecessary risks.
🔹 Set it up, customize your colors, define your UTC offset, and start trading smarter today! 🏆📈
Yearly Profit BackgroundDescription:
The Yearly Profit Background indicator is a powerful tool designed to help traders quickly visualize the profitability of each calendar year on their charts. By analyzing the annual performance of an asset, this indicator colors the background of each completed year green if the year was profitable (close > open) or red if it resulted in a loss (close < open). This visual representation allows traders to identify long-term trends and historical performance at a glance.
Key Features:
Annual Profit Calculation: Automatically calculates the yearly performance based on the opening price of January 1st and the closing price of December 31st.
Visual Background Coloring: Highlights each completed year with a green (profit) or red (loss) background, making it easy to spot trends.
Customizable Transparency: The background colors are set at 90% transparency, ensuring they don’t obstruct your chart analysis.
Optional Price Plots: Displays the annual opening (blue line) and closing (orange line) prices for additional context.
How to Use:
Add the indicator to your chart.
Observe the background colors for each completed year:
Green: The year was profitable.
Red: The year resulted in a loss.
Use the optional price plots to analyze annual opening and closing levels.
Ideal For:
Long-term investors analyzing historical performance.
Traders looking to identify multi-year trends.
Anyone interested in visualizing annual market cycles.
Why Use This Indicator?
Understanding the annual performance of an asset is crucial for making informed trading decisions. The Yearly Profit Background indicator simplifies this process by providing a clear, visual representation of yearly profitability, helping you spot patterns and trends that might otherwise go unnoticed.
Smoothed ROC Z-Score with TableSmoothed ROC Z-Score with Table
This indicator calculates the Rate of Change (ROC) of a chosen price source and transforms it into a smoothed Z-Score oscillator, allowing you to identify market cycle tops and bottoms with reduced noise.
How it works:
The ROC is calculated over a user-defined length.
A moving average and standard deviation over a separate window are used to standardize the ROC into a Z-Score.
This Z-Score is further smoothed using an exponential moving average (EMA) to filter noise and highlight clearer cycle signals.
The smoothed Z-Score oscillates around zero, with upper and lower bands defined by user inputs (default ±2 standard deviations).
When the Z-Score reaches or exceeds ±3 (customizable), the value shown in the table is clamped at ±2 for clearer interpretation.
The indicator plots the smoothed Z-Score line with zero and band lines, and displays a colored Z-Score table on the right for quick reference.
How to read it:
Values near zero indicate neutral momentum.
Rising Z-Scores towards the upper band suggest increasing positive momentum, possible market tops or strength.
Falling Z-Scores towards the lower band indicate negative momentum, potential bottoms or weakness.
The color-coded table gives an easy visual cue: red/orange for strong positive signals, green/teal for strong negative signals, and gray for neutral zones.
Use cases:
Identify turning points in trending markets.
Filter noisy ROC data for cleaner signals.
Combine with other indicators to time entries and exits more effectively.
Maancyclus Volatiliteitsindicator (2025)This Moon Cycle Volatility Indicator for TradingView is designed to help traders track and analyze market volatility around specific lunar phases, namely the Full Moon and New Moon. The indicator marks the dates of these moon phases on the chart and measures volatility using the Average True Range (ATR) indicator, which gauges market price fluctuations.
Key Features:
Moon Phase Markers: The indicator marks the Full Moon and New Moon on the chart using labels. Blue labels are placed below bars for Full Moons, while red labels are placed above bars for New Moons. These markers are based on a manually curated list of moon phase dates for the year 2025.
Volatility Calculation: The indicator calculates market volatility using the ATR (14), which provides a sense of market movement and potential risk. Volatility is plotted as histograms, with blue histograms representing volatility around Full Moons and red histograms around New Moons.
Comparative Analysis: By comparing the volatility around these moon phases to the average volatility, traders can spot potential patterns or heightened market movements. This can inform trading strategies, such as anticipating increased market activity around specific lunar events.
In essence, this tool helps traders identify potential high-volatility periods tied to lunar cycles, which could impact market sentiment and price action.
Simplified STH-MVRV + Z-ScoreSimplified Short Term Holder MVRV (STH-MVRV) + Z-Score Indicator
Description:
This indicator visualizes the Short Term Holder Market Value to Realized Value ratio (STH-MVRV) and its normalized Z-Score, providing insight into Bitcoin’s market cycle phases and potential overbought or oversold conditions.
How it works:
The STH-MVRV ratio compares the market value of coins held by short-term holders to their realized value, helping to identify periods of profit-taking or accumulation by these holders.
The indicator calculates three versions:
STH-MVRV (MVRV): Ratio of current MVRV to its 155-day SMA.
STH-MVRV (Price): Ratio of BTC price to its 155-day SMA.
STH-MVRV (AVG): Average of the above two ratios.
You can select which ratio to display via the input dropdown.
Threshold Lines:
Adjustable upper and lower threshold lines mark significant levels where market sentiment might shift.
The indicator also plots a baseline at 1.0 as a reference.
Z-Score Explanation:
The Z-Score is a normalized value scaled between -3 and +3, calculated relative to the chosen threshold levels.
When the ratio hits the upper threshold, the Z-Score approaches +2, indicating potential overbought conditions.
Conversely, reaching the lower threshold corresponds to a Z-Score near -2, signaling potential oversold conditions.
This Z-Score is shown in a clear table in the top right corner of the chart for easy monitoring.
Data Sources:
MVRV data is fetched from the BTC_MVRV dataset.
Price data is sourced from the BTC/USD index.
Usage:
Use this indicator to assess short-term holder market behavior and to help identify buying or selling opportunities based on extremes indicated by the Z-Score.
Combining this tool with other analysis can improve timing decisions in Bitcoin trading.
Katik Cycle 56 DaysThis script plots vertical dotted lines on the chart every 56 trading days, starting from the first bar. It calculates intervals based on the bar_index and draws the lines for both historical and future dates by projecting the lines forward.
The lines are extended across the entire chart height using extend=extend.both, ensuring visibility regardless of chart zoom level. You can customize the interval length using the input box.
Note: Use this only for 1D (Day) candle so that you can find the changes in the trend...
It Screams When Crypto BottomsGet ready to ride the crypto rollercoaster with your new favourite tool for catching Bitcoin at its juiciest, most oversold moments.
This isn’t just another boring indicator — it screams when it’s time to load your bags and get ready for the ride back up!
Expect it to scream just once or twice per cycle at the very bottom, so you know exactly when the party starts!
Why You'll Love It:
Crypto-Exclusive Magic: It does not really matter what chart you are on; this indicator only bothers about the original and realised market cap of BTC. We all know the rest will follow.
Big Picture Focus: Designed for daily. No noisy intraday drama — just pure, clear signals.
Screaming Alerts: When the signal hits, it’s like a neon sign screaming, “Crypto Bottomed!"
Think of this indicator as your backstage pass to the crypto world’s most dramatic moments. It’s not subtle — it’s bold, loud, and ready to help you time the market like a pro.
P.S.: Use it only on a daily chart. Don’t even try it on shorter timeframes — it won’t scream, and you’ll miss the show! 🙀
AMDX Time ZoneThis script is base on the theory of @traderdaye, on the TimeZone AMDX
Accumulation
Manipulation
Distribution
X reversal / continuation
OR
AMDX
It show you the box on intraday Timeframe:
Q1: 18.00 - 19.30 | Q2: 19.30 - 21.00 | Q3: 21.00 - 22.30 | Q4: 22.30 - 00.00 (90min Cycles of the Asian Session)
Q1: 00.00 - 01.30 | Q2: 01.30 - 03.00 | Q3: 03.00 - 04.30 | Q4: 04.30 - 06.00 (90min Cycles of the London Session)
Q1: 06.00 - 07.30 | Q2: 07.30 - 09.00 | Q3: 09.00 - 10.30 | Q4: 10.30 - 12.00 (90min Cycles of the NY Session)
Q1: 12.00 - 13.30 | Q2: 13.30 - 15.00 | Q3: 15.00 - 16.30 | Q4: 16.30 - 18.00 (90min Cycles of the PM Session)
You can extend this theory to the day => to the week => to the month
Thanks LuxAlgo for the base,
Hope you enjoy it
OPEX & VIX Expiry Markers (Past, Present, Future)Expiry Date Indicator for Options & Index Traders
Track Key Expiration Dates Automatically
For traders focused on options, indices, and expiration-based strategies, staying aware of key expiration dates is essential. This TradingView indicator automatically plots OPEX, VIX Expiry, and Quarterly Expirations on your charts—helping you plan trades more effectively without manual tracking.
Features:
✔ OPEX Expiration Markers – Highlights the third Friday of each month, when equity and index options expire.
✔ VIX Expiration Tracking – Marks Wednesday VIX expirations, useful for volatility-based trades.
✔ Quarterly Expiration Highlights – Identifies major market expiration cycles for better trade management.
✔ Live Countdown to Next OPEX – Displays how many days remain until the next expiration.
✔ Works on Any Timeframe – Past, present, and future expiration dates update dynamically.
✔ Customizable Settings – Enable or disable specific features based on your trading style.
Ideal for Traders Who Use:
📈 SPX / SPY / NDX / VIX Options Strategies
📅 Iron Condors, Credit Spreads, and Expiration-Based Trades
This tool helps traders stay ahead of expiration cycles, ensuring they never miss an important date. Simple, effective, and built for seamless integration into your trading workflow.
This keeps it professional and to the point without overhyping it. Let me know if you'd like any further refinements! 🚀
Goertzel Browser [Loxx]As the financial markets become increasingly complex and data-driven, traders and analysts must leverage powerful tools to gain insights and make informed decisions. One such tool is the Goertzel Browser indicator, a sophisticated technical analysis indicator that helps identify cyclical patterns in financial data. This powerful tool is capable of detecting cyclical patterns in financial data, helping traders to make better predictions and optimize their trading strategies. With its unique combination of mathematical algorithms and advanced charting capabilities, this indicator has the potential to revolutionize the way we approach financial modeling and trading.
█ Brief Overview of the Goertzel Browser
The Goertzel Browser is a sophisticated technical analysis tool that utilizes the Goertzel algorithm to analyze and visualize cyclical components within a financial time series. By identifying these cycles and their characteristics, the indicator aims to provide valuable insights into the market's underlying price movements, which could potentially be used for making informed trading decisions.
The primary purpose of this indicator is to:
1. Detect and analyze the dominant cycles present in the price data.
2. Reconstruct and visualize the composite wave based on the detected cycles.
3. Project the composite wave into the future, providing a potential roadmap for upcoming price movements.
To achieve this, the indicator performs several tasks:
1. Detrending the price data: The indicator preprocesses the price data using various detrending techniques, such as Hodrick-Prescott filters, zero-lag moving averages, and linear regression, to remove the underlying trend and focus on the cyclical components.
2. Applying the Goertzel algorithm: The indicator applies the Goertzel algorithm to the detrended price data, identifying the dominant cycles and their characteristics, such as amplitude, phase, and cycle strength.
3. Constructing the composite wave: The indicator reconstructs the composite wave by combining the detected cycles, either by using a user-defined list of cycles or by selecting the top N cycles based on their amplitude or cycle strength.
4. Visualizing the composite wave: The indicator plots the composite wave, using solid lines for the past and dotted lines for the future projections. The color of the lines indicates whether the wave is increasing or decreasing.
5. Displaying cycle information: The indicator provides a table that displays detailed information about the detected cycles, including their rank, period, Bartel's test results, amplitude, and phase.
This indicator is a powerful tool that employs the Goertzel algorithm to analyze and visualize the cyclical components within a financial time series. By providing insights into the underlying price movements and their potential future trajectory, the indicator aims to assist traders in making more informed decisions.
█ What is the Goertzel Algorithm?
The Goertzel algorithm, named after Gerald Goertzel, is a digital signal processing technique that is used to efficiently compute individual terms of the Discrete Fourier Transform (DFT). It was first introduced in 1958, and since then, it has found various applications in the fields of engineering, mathematics, and physics.
The Goertzel algorithm is primarily used to detect specific frequency components within a digital signal, making it particularly useful in applications where only a few frequency components are of interest. The algorithm is computationally efficient, as it requires fewer calculations than the Fast Fourier Transform (FFT) when detecting a small number of frequency components. This efficiency makes the Goertzel algorithm a popular choice in applications such as:
1. Telecommunications: The Goertzel algorithm is used for decoding Dual-Tone Multi-Frequency (DTMF) signals, which are the tones generated when pressing buttons on a telephone keypad. By identifying specific frequency components, the algorithm can accurately determine which button has been pressed.
2. Audio processing: The algorithm can be used to detect specific pitches or harmonics in an audio signal, making it useful in applications like pitch detection and tuning musical instruments.
3. Vibration analysis: In the field of mechanical engineering, the Goertzel algorithm can be applied to analyze vibrations in rotating machinery, helping to identify faulty components or signs of wear.
4. Power system analysis: The algorithm can be used to measure harmonic content in power systems, allowing engineers to assess power quality and detect potential issues.
The Goertzel algorithm is used in these applications because it offers several advantages over other methods, such as the FFT:
1. Computational efficiency: The Goertzel algorithm requires fewer calculations when detecting a small number of frequency components, making it more computationally efficient than the FFT in these cases.
2. Real-time analysis: The algorithm can be implemented in a streaming fashion, allowing for real-time analysis of signals, which is crucial in applications like telecommunications and audio processing.
3. Memory efficiency: The Goertzel algorithm requires less memory than the FFT, as it only computes the frequency components of interest.
4. Precision: The algorithm is less susceptible to numerical errors compared to the FFT, ensuring more accurate results in applications where precision is essential.
The Goertzel algorithm is an efficient digital signal processing technique that is primarily used to detect specific frequency components within a signal. Its computational efficiency, real-time capabilities, and precision make it an attractive choice for various applications, including telecommunications, audio processing, vibration analysis, and power system analysis. The algorithm has been widely adopted since its introduction in 1958 and continues to be an essential tool in the fields of engineering, mathematics, and physics.
█ Goertzel Algorithm in Quantitative Finance: In-Depth Analysis and Applications
The Goertzel algorithm, initially designed for signal processing in telecommunications, has gained significant traction in the financial industry due to its efficient frequency detection capabilities. In quantitative finance, the Goertzel algorithm has been utilized for uncovering hidden market cycles, developing data-driven trading strategies, and optimizing risk management. This section delves deeper into the applications of the Goertzel algorithm in finance, particularly within the context of quantitative trading and analysis.
Unveiling Hidden Market Cycles:
Market cycles are prevalent in financial markets and arise from various factors, such as economic conditions, investor psychology, and market participant behavior. The Goertzel algorithm's ability to detect and isolate specific frequencies in price data helps trader analysts identify hidden market cycles that may otherwise go unnoticed. By examining the amplitude, phase, and periodicity of each cycle, traders can better understand the underlying market structure and dynamics, enabling them to develop more informed and effective trading strategies.
Developing Quantitative Trading Strategies:
The Goertzel algorithm's versatility allows traders to incorporate its insights into a wide range of trading strategies. By identifying the dominant market cycles in a financial instrument's price data, traders can create data-driven strategies that capitalize on the cyclical nature of markets.
For instance, a trader may develop a mean-reversion strategy that takes advantage of the identified cycles. By establishing positions when the price deviates from the predicted cycle, the trader can profit from the subsequent reversion to the cycle's mean. Similarly, a momentum-based strategy could be designed to exploit the persistence of a dominant cycle by entering positions that align with the cycle's direction.
Enhancing Risk Management:
The Goertzel algorithm plays a vital role in risk management for quantitative strategies. By analyzing the cyclical components of a financial instrument's price data, traders can gain insights into the potential risks associated with their trading strategies.
By monitoring the amplitude and phase of dominant cycles, a trader can detect changes in market dynamics that may pose risks to their positions. For example, a sudden increase in amplitude may indicate heightened volatility, prompting the trader to adjust position sizing or employ hedging techniques to protect their portfolio. Additionally, changes in phase alignment could signal a potential shift in market sentiment, necessitating adjustments to the trading strategy.
Expanding Quantitative Toolkits:
Traders can augment the Goertzel algorithm's insights by combining it with other quantitative techniques, creating a more comprehensive and sophisticated analysis framework. For example, machine learning algorithms, such as neural networks or support vector machines, could be trained on features extracted from the Goertzel algorithm to predict future price movements more accurately.
Furthermore, the Goertzel algorithm can be integrated with other technical analysis tools, such as moving averages or oscillators, to enhance their effectiveness. By applying these tools to the identified cycles, traders can generate more robust and reliable trading signals.
The Goertzel algorithm offers invaluable benefits to quantitative finance practitioners by uncovering hidden market cycles, aiding in the development of data-driven trading strategies, and improving risk management. By leveraging the insights provided by the Goertzel algorithm and integrating it with other quantitative techniques, traders can gain a deeper understanding of market dynamics and devise more effective trading strategies.
█ Indicator Inputs
src: This is the source data for the analysis, typically the closing price of the financial instrument.
detrendornot: This input determines the method used for detrending the source data. Detrending is the process of removing the underlying trend from the data to focus on the cyclical components.
The available options are:
hpsmthdt: Detrend using Hodrick-Prescott filter centered moving average.
zlagsmthdt: Detrend using zero-lag moving average centered moving average.
logZlagRegression: Detrend using logarithmic zero-lag linear regression.
hpsmth: Detrend using Hodrick-Prescott filter.
zlagsmth: Detrend using zero-lag moving average.
DT_HPper1 and DT_HPper2: These inputs define the period range for the Hodrick-Prescott filter centered moving average when detrendornot is set to hpsmthdt.
DT_ZLper1 and DT_ZLper2: These inputs define the period range for the zero-lag moving average centered moving average when detrendornot is set to zlagsmthdt.
DT_RegZLsmoothPer: This input defines the period for the zero-lag moving average used in logarithmic zero-lag linear regression when detrendornot is set to logZlagRegression.
HPsmoothPer: This input defines the period for the Hodrick-Prescott filter when detrendornot is set to hpsmth.
ZLMAsmoothPer: This input defines the period for the zero-lag moving average when detrendornot is set to zlagsmth.
MaxPer: This input sets the maximum period for the Goertzel algorithm to search for cycles.
squaredAmp: This boolean input determines whether the amplitude should be squared in the Goertzel algorithm.
useAddition: This boolean input determines whether the Goertzel algorithm should use addition for combining the cycles.
useCosine: This boolean input determines whether the Goertzel algorithm should use cosine waves instead of sine waves.
UseCycleStrength: This boolean input determines whether the Goertzel algorithm should compute the cycle strength, which is a normalized measure of the cycle's amplitude.
WindowSizePast and WindowSizeFuture: These inputs define the window size for past and future projections of the composite wave.
FilterBartels: This boolean input determines whether Bartel's test should be applied to filter out non-significant cycles.
BartNoCycles: This input sets the number of cycles to be used in Bartel's test.
BartSmoothPer: This input sets the period for the moving average used in Bartel's test.
BartSigLimit: This input sets the significance limit for Bartel's test, below which cycles are considered insignificant.
SortBartels: This boolean input determines whether the cycles should be sorted by their Bartel's test results.
UseCycleList: This boolean input determines whether a user-defined list of cycles should be used for constructing the composite wave. If set to false, the top N cycles will be used.
Cycle1, Cycle2, Cycle3, Cycle4, and Cycle5: These inputs define the user-defined list of cycles when 'UseCycleList' is set to true. If using a user-defined list, each of these inputs represents the period of a specific cycle to include in the composite wave.
StartAtCycle: This input determines the starting index for selecting the top N cycles when UseCycleList is set to false. This allows you to skip a certain number of cycles from the top before selecting the desired number of cycles.
UseTopCycles: This input sets the number of top cycles to use for constructing the composite wave when UseCycleList is set to false. The cycles are ranked based on their amplitudes or cycle strengths, depending on the UseCycleStrength input.
SubtractNoise: This boolean input determines whether to subtract the noise (remaining cycles) from the composite wave. If set to true, the composite wave will only include the top N cycles specified by UseTopCycles.
█ Exploring Auxiliary Functions
The following functions demonstrate advanced techniques for analyzing financial markets, including zero-lag moving averages, Bartels probability, detrending, and Hodrick-Prescott filtering. This section examines each function in detail, explaining their purpose, methodology, and applications in finance. We will examine how each function contributes to the overall performance and effectiveness of the indicator and how they work together to create a powerful analytical tool.
Zero-Lag Moving Average:
The zero-lag moving average function is designed to minimize the lag typically associated with moving averages. This is achieved through a two-step weighted linear regression process that emphasizes more recent data points. The function calculates a linearly weighted moving average (LWMA) on the input data and then applies another LWMA on the result. By doing this, the function creates a moving average that closely follows the price action, reducing the lag and improving the responsiveness of the indicator.
The zero-lag moving average function is used in the indicator to provide a responsive, low-lag smoothing of the input data. This function helps reduce the noise and fluctuations in the data, making it easier to identify and analyze underlying trends and patterns. By minimizing the lag associated with traditional moving averages, this function allows the indicator to react more quickly to changes in market conditions, providing timely signals and improving the overall effectiveness of the indicator.
Bartels Probability:
The Bartels probability function calculates the probability of a given cycle being significant in a time series. It uses a mathematical test called the Bartels test to assess the significance of cycles detected in the data. The function calculates coefficients for each detected cycle and computes an average amplitude and an expected amplitude. By comparing these values, the Bartels probability is derived, indicating the likelihood of a cycle's significance. This information can help in identifying and analyzing dominant cycles in financial markets.
The Bartels probability function is incorporated into the indicator to assess the significance of detected cycles in the input data. By calculating the Bartels probability for each cycle, the indicator can prioritize the most significant cycles and focus on the market dynamics that are most relevant to the current trading environment. This function enhances the indicator's ability to identify dominant market cycles, improving its predictive power and aiding in the development of effective trading strategies.
Detrend Logarithmic Zero-Lag Regression:
The detrend logarithmic zero-lag regression function is used for detrending data while minimizing lag. It combines a zero-lag moving average with a linear regression detrending method. The function first calculates the zero-lag moving average of the logarithm of input data and then applies a linear regression to remove the trend. By detrending the data, the function isolates the cyclical components, making it easier to analyze and interpret the underlying market dynamics.
The detrend logarithmic zero-lag regression function is used in the indicator to isolate the cyclical components of the input data. By detrending the data, the function enables the indicator to focus on the cyclical movements in the market, making it easier to analyze and interpret market dynamics. This function is essential for identifying cyclical patterns and understanding the interactions between different market cycles, which can inform trading decisions and enhance overall market understanding.
Bartels Cycle Significance Test:
The Bartels cycle significance test is a function that combines the Bartels probability function and the detrend logarithmic zero-lag regression function to assess the significance of detected cycles. The function calculates the Bartels probability for each cycle and stores the results in an array. By analyzing the probability values, traders and analysts can identify the most significant cycles in the data, which can be used to develop trading strategies and improve market understanding.
The Bartels cycle significance test function is integrated into the indicator to provide a comprehensive analysis of the significance of detected cycles. By combining the Bartels probability function and the detrend logarithmic zero-lag regression function, this test evaluates the significance of each cycle and stores the results in an array. The indicator can then use this information to prioritize the most significant cycles and focus on the most relevant market dynamics. This function enhances the indicator's ability to identify and analyze dominant market cycles, providing valuable insights for trading and market analysis.
Hodrick-Prescott Filter:
The Hodrick-Prescott filter is a popular technique used to separate the trend and cyclical components of a time series. The function applies a smoothing parameter to the input data and calculates a smoothed series using a two-sided filter. This smoothed series represents the trend component, which can be subtracted from the original data to obtain the cyclical component. The Hodrick-Prescott filter is commonly used in economics and finance to analyze economic data and financial market trends.
The Hodrick-Prescott filter is incorporated into the indicator to separate the trend and cyclical components of the input data. By applying the filter to the data, the indicator can isolate the trend component, which can be used to analyze long-term market trends and inform trading decisions. Additionally, the cyclical component can be used to identify shorter-term market dynamics and provide insights into potential trading opportunities. The inclusion of the Hodrick-Prescott filter adds another layer of analysis to the indicator, making it more versatile and comprehensive.
Detrending Options: Detrend Centered Moving Average:
The detrend centered moving average function provides different detrending methods, including the Hodrick-Prescott filter and the zero-lag moving average, based on the selected detrending method. The function calculates two sets of smoothed values using the chosen method and subtracts one set from the other to obtain a detrended series. By offering multiple detrending options, this function allows traders and analysts to select the most appropriate method for their specific needs and preferences.
The detrend centered moving average function is integrated into the indicator to provide users with multiple detrending options, including the Hodrick-Prescott filter and the zero-lag moving average. By offering multiple detrending methods, the indicator allows users to customize the analysis to their specific needs and preferences, enhancing the indicator's overall utility and adaptability. This function ensures that the indicator can cater to a wide range of trading styles and objectives, making it a valuable tool for a diverse group of market participants.
The auxiliary functions functions discussed in this section demonstrate the power and versatility of mathematical techniques in analyzing financial markets. By understanding and implementing these functions, traders and analysts can gain valuable insights into market dynamics, improve their trading strategies, and make more informed decisions. The combination of zero-lag moving averages, Bartels probability, detrending methods, and the Hodrick-Prescott filter provides a comprehensive toolkit for analyzing and interpreting financial data. The integration of advanced functions in a financial indicator creates a powerful and versatile analytical tool that can provide valuable insights into financial markets. By combining the zero-lag moving average,
█ In-Depth Analysis of the Goertzel Browser Code
The Goertzel Browser code is an implementation of the Goertzel Algorithm, an efficient technique to perform spectral analysis on a signal. The code is designed to detect and analyze dominant cycles within a given financial market data set. This section will provide an extremely detailed explanation of the code, its structure, functions, and intended purpose.
Function signature and input parameters:
The Goertzel Browser function accepts numerous input parameters for customization, including source data (src), the current bar (forBar), sample size (samplesize), period (per), squared amplitude flag (squaredAmp), addition flag (useAddition), cosine flag (useCosine), cycle strength flag (UseCycleStrength), past and future window sizes (WindowSizePast, WindowSizeFuture), Bartels filter flag (FilterBartels), Bartels-related parameters (BartNoCycles, BartSmoothPer, BartSigLimit), sorting flag (SortBartels), and output buffers (goeWorkPast, goeWorkFuture, cyclebuffer, amplitudebuffer, phasebuffer, cycleBartelsBuffer).
Initializing variables and arrays:
The code initializes several float arrays (goeWork1, goeWork2, goeWork3, goeWork4) with the same length as twice the period (2 * per). These arrays store intermediate results during the execution of the algorithm.
Preprocessing input data:
The input data (src) undergoes preprocessing to remove linear trends. This step enhances the algorithm's ability to focus on cyclical components in the data. The linear trend is calculated by finding the slope between the first and last values of the input data within the sample.
Iterative calculation of Goertzel coefficients:
The core of the Goertzel Browser algorithm lies in the iterative calculation of Goertzel coefficients for each frequency bin. These coefficients represent the spectral content of the input data at different frequencies. The code iterates through the range of frequencies, calculating the Goertzel coefficients using a nested loop structure.
Cycle strength computation:
The code calculates the cycle strength based on the Goertzel coefficients. This is an optional step, controlled by the UseCycleStrength flag. The cycle strength provides information on the relative influence of each cycle on the data per bar, considering both amplitude and cycle length. The algorithm computes the cycle strength either by squaring the amplitude (controlled by squaredAmp flag) or using the actual amplitude values.
Phase calculation:
The Goertzel Browser code computes the phase of each cycle, which represents the position of the cycle within the input data. The phase is calculated using the arctangent function (math.atan) based on the ratio of the imaginary and real components of the Goertzel coefficients.
Peak detection and cycle extraction:
The algorithm performs peak detection on the computed amplitudes or cycle strengths to identify dominant cycles. It stores the detected cycles in the cyclebuffer array, along with their corresponding amplitudes and phases in the amplitudebuffer and phasebuffer arrays, respectively.
Sorting cycles by amplitude or cycle strength:
The code sorts the detected cycles based on their amplitude or cycle strength in descending order. This allows the algorithm to prioritize cycles with the most significant impact on the input data.
Bartels cycle significance test:
If the FilterBartels flag is set, the code performs a Bartels cycle significance test on the detected cycles. This test determines the statistical significance of each cycle and filters out the insignificant cycles. The significant cycles are stored in the cycleBartelsBuffer array. If the SortBartels flag is set, the code sorts the significant cycles based on their Bartels significance values.
Waveform calculation:
The Goertzel Browser code calculates the waveform of the significant cycles for both past and future time windows. The past and future windows are defined by the WindowSizePast and WindowSizeFuture parameters, respectively. The algorithm uses either cosine or sine functions (controlled by the useCosine flag) to calculate the waveforms for each cycle. The useAddition flag determines whether the waveforms should be added or subtracted.
Storing waveforms in matrices:
The calculated waveforms for each cycle are stored in two matrices - goeWorkPast and goeWorkFuture. These matrices hold the waveforms for the past and future time windows, respectively. Each row in the matrices represents a time window position, and each column corresponds to a cycle.
Returning the number of cycles:
The Goertzel Browser function returns the total number of detected cycles (number_of_cycles) after processing the input data. This information can be used to further analyze the results or to visualize the detected cycles.
The Goertzel Browser code is a comprehensive implementation of the Goertzel Algorithm, specifically designed for detecting and analyzing dominant cycles within financial market data. The code offers a high level of customization, allowing users to fine-tune the algorithm based on their specific needs. The Goertzel Browser's combination of preprocessing, iterative calculations, cycle extraction, sorting, significance testing, and waveform calculation makes it a powerful tool for understanding cyclical components in financial data.
█ Generating and Visualizing Composite Waveform
The indicator calculates and visualizes the composite waveform for both past and future time windows based on the detected cycles. Here's a detailed explanation of this process:
Updating WindowSizePast and WindowSizeFuture:
The WindowSizePast and WindowSizeFuture are updated to ensure they are at least twice the MaxPer (maximum period).
Initializing matrices and arrays:
Two matrices, goeWorkPast and goeWorkFuture, are initialized to store the Goertzel results for past and future time windows. Multiple arrays are also initialized to store cycle, amplitude, phase, and Bartels information.
Preparing the source data (srcVal) array:
The source data is copied into an array, srcVal, and detrended using one of the selected methods (hpsmthdt, zlagsmthdt, logZlagRegression, hpsmth, or zlagsmth).
Goertzel function call:
The Goertzel function is called to analyze the detrended source data and extract cycle information. The output, number_of_cycles, contains the number of detected cycles.
Initializing arrays for past and future waveforms:
Three arrays, epgoertzel, goertzel, and goertzelFuture, are initialized to store the endpoint Goertzel, non-endpoint Goertzel, and future Goertzel projections, respectively.
Calculating composite waveform for past bars (goertzel array):
The past composite waveform is calculated by summing the selected cycles (either from the user-defined cycle list or the top cycles) and optionally subtracting the noise component.
Calculating composite waveform for future bars (goertzelFuture array):
The future composite waveform is calculated in a similar way as the past composite waveform.
Drawing past composite waveform (pvlines):
The past composite waveform is drawn on the chart using solid lines. The color of the lines is determined by the direction of the waveform (green for upward, red for downward).
Drawing future composite waveform (fvlines):
The future composite waveform is drawn on the chart using dotted lines. The color of the lines is determined by the direction of the waveform (fuchsia for upward, yellow for downward).
Displaying cycle information in a table (table3):
A table is created to display the cycle information, including the rank, period, Bartel value, amplitude (or cycle strength), and phase of each detected cycle.
Filling the table with cycle information:
The indicator iterates through the detected cycles and retrieves the relevant information (period, amplitude, phase, and Bartel value) from the corresponding arrays. It then fills the table with this information, displaying the values up to six decimal places.
To summarize, this indicator generates a composite waveform based on the detected cycles in the financial data. It calculates the composite waveforms for both past and future time windows and visualizes them on the chart using colored lines. Additionally, it displays detailed cycle information in a table, including the rank, period, Bartel value, amplitude (or cycle strength), and phase of each detected cycle.
█ Enhancing the Goertzel Algorithm-Based Script for Financial Modeling and Trading
The Goertzel algorithm-based script for detecting dominant cycles in financial data is a powerful tool for financial modeling and trading. It provides valuable insights into the past behavior of these cycles and potential future impact. However, as with any algorithm, there is always room for improvement. This section discusses potential enhancements to the existing script to make it even more robust and versatile for financial modeling, general trading, advanced trading, and high-frequency finance trading.
Enhancements for Financial Modeling
Data preprocessing: One way to improve the script's performance for financial modeling is to introduce more advanced data preprocessing techniques. This could include removing outliers, handling missing data, and normalizing the data to ensure consistent and accurate results.
Additional detrending and smoothing methods: Incorporating more sophisticated detrending and smoothing techniques, such as wavelet transform or empirical mode decomposition, can help improve the script's ability to accurately identify cycles and trends in the data.
Machine learning integration: Integrating machine learning techniques, such as artificial neural networks or support vector machines, can help enhance the script's predictive capabilities, leading to more accurate financial models.
Enhancements for General and Advanced Trading
Customizable indicator integration: Allowing users to integrate their own technical indicators can help improve the script's effectiveness for both general and advanced trading. By enabling the combination of the dominant cycle information with other technical analysis tools, traders can develop more comprehensive trading strategies.
Risk management and position sizing: Incorporating risk management and position sizing functionality into the script can help traders better manage their trades and control potential losses. This can be achieved by calculating the optimal position size based on the user's risk tolerance and account size.
Multi-timeframe analysis: Enhancing the script to perform multi-timeframe analysis can provide traders with a more holistic view of market trends and cycles. By identifying dominant cycles on different timeframes, traders can gain insights into the potential confluence of cycles and make better-informed trading decisions.
Enhancements for High-Frequency Finance Trading
Algorithm optimization: To ensure the script's suitability for high-frequency finance trading, optimizing the algorithm for faster execution is crucial. This can be achieved by employing efficient data structures and refining the calculation methods to minimize computational complexity.
Real-time data streaming: Integrating real-time data streaming capabilities into the script can help high-frequency traders react to market changes more quickly. By continuously updating the cycle information based on real-time market data, traders can adapt their strategies accordingly and capitalize on short-term market fluctuations.
Order execution and trade management: To fully leverage the script's capabilities for high-frequency trading, implementing functionality for automated order execution and trade management is essential. This can include features such as stop-loss and take-profit orders, trailing stops, and automated trade exit strategies.
While the existing Goertzel algorithm-based script is a valuable tool for detecting dominant cycles in financial data, there are several potential enhancements that can make it even more powerful for financial modeling, general trading, advanced trading, and high-frequency finance trading. By incorporating these improvements, the script can become a more versatile and effective tool for traders and financial analysts alike.
█ Understanding the Limitations of the Goertzel Algorithm
While the Goertzel algorithm-based script for detecting dominant cycles in financial data provides valuable insights, it is important to be aware of its limitations and drawbacks. Some of the key drawbacks of this indicator are:
Lagging nature:
As with many other technical indicators, the Goertzel algorithm-based script can suffer from lagging effects, meaning that it may not immediately react to real-time market changes. This lag can lead to late entries and exits, potentially resulting in reduced profitability or increased losses.
Parameter sensitivity:
The performance of the script can be sensitive to the chosen parameters, such as the detrending methods, smoothing techniques, and cycle detection settings. Improper parameter selection may lead to inaccurate cycle detection or increased false signals, which can negatively impact trading performance.
Complexity:
The Goertzel algorithm itself is relatively complex, making it difficult for novice traders or those unfamiliar with the concept of cycle analysis to fully understand and effectively utilize the script. This complexity can also make it challenging to optimize the script for specific trading styles or market conditions.
Overfitting risk:
As with any data-driven approach, there is a risk of overfitting when using the Goertzel algorithm-based script. Overfitting occurs when a model becomes too specific to the historical data it was trained on, leading to poor performance on new, unseen data. This can result in misleading signals and reduced trading performance.
No guarantee of future performance: While the script can provide insights into past cycles and potential future trends, it is important to remember that past performance does not guarantee future results. Market conditions can change, and relying solely on the script's predictions without considering other factors may lead to poor trading decisions.
Limited applicability: The Goertzel algorithm-based script may not be suitable for all markets, trading styles, or timeframes. Its effectiveness in detecting cycles may be limited in certain market conditions, such as during periods of extreme volatility or low liquidity.
While the Goertzel algorithm-based script offers valuable insights into dominant cycles in financial data, it is essential to consider its drawbacks and limitations when incorporating it into a trading strategy. Traders should always use the script in conjunction with other technical and fundamental analysis tools, as well as proper risk management, to make well-informed trading decisions.
█ Interpreting Results
The Goertzel Browser indicator can be interpreted by analyzing the plotted lines and the table presented alongside them. The indicator plots two lines: past and future composite waves. The past composite wave represents the composite wave of the past price data, and the future composite wave represents the projected composite wave for the next period.
The past composite wave line displays a solid line, with green indicating a bullish trend and red indicating a bearish trend. On the other hand, the future composite wave line is a dotted line with fuchsia indicating a bullish trend and yellow indicating a bearish trend.
The table presented alongside the indicator shows the top cycles with their corresponding rank, period, Bartels, amplitude or cycle strength, and phase. The amplitude is a measure of the strength of the cycle, while the phase is the position of the cycle within the data series.
Interpreting the Goertzel Browser indicator involves identifying the trend of the past and future composite wave lines and matching them with the corresponding bullish or bearish color. Additionally, traders can identify the top cycles with the highest amplitude or cycle strength and utilize them in conjunction with other technical indicators and fundamental analysis for trading decisions.
This indicator is considered a repainting indicator because the value of the indicator is calculated based on the past price data. As new price data becomes available, the indicator's value is recalculated, potentially causing the indicator's past values to change. This can create a false impression of the indicator's performance, as it may appear to have provided a profitable trading signal in the past when, in fact, that signal did not exist at the time.
The Goertzel indicator is also non-endpointed, meaning that it is not calculated up to the current bar or candle. Instead, it uses a fixed amount of historical data to calculate its values, which can make it difficult to use for real-time trading decisions. For example, if the indicator uses 100 bars of historical data to make its calculations, it cannot provide a signal until the current bar has closed and become part of the historical data. This can result in missed trading opportunities or delayed signals.
█ Conclusion
The Goertzel Browser indicator is a powerful tool for identifying and analyzing cyclical patterns in financial markets. Its ability to detect multiple cycles of varying frequencies and strengths make it a valuable addition to any trader's technical analysis toolkit. However, it is important to keep in mind that the Goertzel Browser indicator should be used in conjunction with other technical analysis tools and fundamental analysis to achieve the best results. With continued refinement and development, the Goertzel Browser indicator has the potential to become a highly effective tool for financial modeling, general trading, advanced trading, and high-frequency finance trading. Its accuracy and versatility make it a promising candidate for further research and development.
█ Footnotes
What is the Bartels Test for Cycle Significance?
The Bartels Cycle Significance Test is a statistical method that determines whether the peaks and troughs of a time series are statistically significant. The test is named after its inventor, George Bartels, who developed it in the mid-20th century.
The Bartels test is designed to analyze the cyclical components of a time series, which can help traders and analysts identify trends and cycles in financial markets. The test calculates a Bartels statistic, which measures the degree of non-randomness or autocorrelation in the time series.
The Bartels statistic is calculated by first splitting the time series into two halves and calculating the range of the peaks and troughs in each half. The test then compares these ranges using a t-test, which measures the significance of the difference between the two ranges.
If the Bartels statistic is greater than a critical value, it indicates that the peaks and troughs in the time series are non-random and that there is a significant cyclical component to the data. Conversely, if the Bartels statistic is less than the critical value, it suggests that the peaks and troughs are random and that there is no significant cyclical component.
The Bartels Cycle Significance Test is particularly useful in financial analysis because it can help traders and analysts identify significant cycles in asset prices, which can in turn inform investment decisions. However, it is important to note that the test is not perfect and can produce false signals in certain situations, particularly in noisy or volatile markets. Therefore, it is always recommended to use the test in conjunction with other technical and fundamental indicators to confirm trends and cycles.
Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
The first term represents the deviation of the data from the trend.
The second term represents the smoothness of the trend.
λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
Ichimoku Theories [LuxAlgo]The Ichimoku Theories indicator is the most complete Ichimoku tool you will ever need. Four tools combined into one to harness all the power of Ichimoku Kinkō Hyō.
This tool features the following concepts based on the work of Goichi Hosoda:
Ichimoku Kinkō Hyō: Original Ichimoku indicator with its five main lines and kumo.
Time Theory: automatic time cycle identification and forecasting to understand market timing.
Wave Theory: automatic wave identification to understand market structure.
Price Theory: automatic identification of developing N waves and possible price targets to understand future price behavior.
🔶 ICHIMOKU KINKŌ HYŌ
Ichimoku with lines only, Kumo only and both together
Let us start with the basics: the Ichimoku original indicator is a tool to understand the market, not to predict it, it is a trend-following tool, so it is best used in trending markets.
Ichimoku tells us what is happening in the market and what may happen next, the aim of the tool is to provide market understanding, not trading signals.
The tool is based on calculating the mid-point between the high and low of three pre-defined ranges as the equilibrium price for short (9 periods), medium (26 periods), and long (52 periods) time horizons:
Tenkan sen: middle point of the range of the last 9 candles
Kinjun sen: middle point of the range of the last 26 candles
Senkou span A: middle point between Tankan Sen and Kijun Sen, plotted 26 candles into the future
Senkou span B: midpoint of the range of the last 52 candles, plotted 26 candles into the future
Chikou span: closing price plotted 26 candles into the past
Kumo: area between Senkou pans A and B (kumo means cloud in Japanese)
The most basic use of the tool is to use the Kumo as an area of possible support or resistance.
🔶 TIME THEORY
Current cycles and forecast
Time theory is a critical concept used to identify historical and current market cycles, and use these to forecast the next ones. This concept is based on the Kihon Suchi (translating to "Basic Numbers" in Japanese), these are 9 and 26, and from their combinations we obtain the following sequence:
9, 17, 26, 33, 42, 51, 65, 76, 129, 172, 200, 257
The main idea is that the market moves in cycles with periods set by the Kihon Suchi sequence.
When the cycle has the same exact periods, we obtain the Taito Suchi (translating to "Same Number" in Japanese).
This tool allows traders to identify historical and current market cycles and forecast the next one.
🔹 Time Cycle Identification
Presentation of 4 different modes: SWINGS, HIGHS, KINJUN, and WAVES .
The tool draws a horizontal line at the bottom of the chart showing the cycles detected and their size.
The following settings are used:
Time Cycle Mode: up to 7 different modes
Wave Cycle: Which wave to use when WAVE mode is selected, only active waves in the Wave Theory settings will be used.
Show Time Cycles: keep a cleaner chart by disabling cycles visualisation
Show last X time cycles: how many cycles to display
🔹 Time Cycle Forecast
Showcasing the two forecasting patterns: Kihon Suchi and Taito Suchi
The tool plots horizontal lines, a solid anchor line, and several dotted forecast lines.
The following settings are used:
Show time cycle forecast: to keep things clean
Forecast Pattern: comes in two flavors
Kihon Suchi plots a line from the anchor at each number in the Kihon Suchi sequence.
Taito Suchi plot lines from the anchor with the same size detected in the anchored cycle
Anchor forecast on last X time cycle: traders can place the anchor in any detected cycle
🔶 WAVE THEORY
All waves activated with overlapping
The main idea behind this theory is that markets move like waves in the sea, back and forth (making swing lows and highs). Understanding the current market structure is key to having realistic expectations of what the market may do next. The waves are divided into Simple and Complex.
The following settings are used:
Basic Waves: allows traders to activate waves I, V and N
Complex Waves: allows traders to activate waves P, Y and W
Overlapping waves: to avoid missing out on any of the waves activated
Show last X waves: how many waves will be displayed
🔹 Basic Waves
The three basic waves
The basic waves from which all waves are made are I, V, and N
I wave: one leg moves
V wave: two legs move, one against the other
N wave: Three legs move, push, pull back, and another push
🔹 Complex Waves
Three complex waves
There are other waves like
P wave: contracting market
Y wave: expanding market
W wave: double top or double bottom
🔶 PRICE THEORY
All targets for the current N wave with their calculations
This theory is based on identifying developing N waves and predicting potential price targets based on that developing wave.
The tool displays 4 basic targets (V, E, N, and NT) and 3 extended targets (2E and 3E) according to the calculations shown in the chart above. Traders can enable or disable each target in the settings panel.
🔶 USING EVERYTHING TOGETHER
Please DON'T do this. This is not how you use it
Now the real example:
Daily chart of Nasdaq 100 futures (NQ1!) with our Ichimoku analysis
Time, waves, and price theories go together as one:
First, we identify the current time cycles and wave structure.
Then we forecast the next cycle and possible key price levels.
We identify a Taito Suchi with both legs of exactly 41 candles on each I wave, both together forming a V wave, the last two I waves are part of a developing N wave, and the time cycle of the first one is 191 candles. We forecast this cycle into the future and get 22nd April as a key date, so in 6 trading days (as of this writing) the market would have completed another Taito Suchi pattern if a new wave and time cycle starts. As we have a developing N wave we can see the potential price targets, the price is actually between the NT and V targets. We have a bullish Kumo and the price is touching it, if this Kumo provides enough support for the price to go further, the market could reach N or E targets.
So we have identified the cycle and wave, our expectations are that the current cycle is another Taito Suchi and the current wave is an N wave, the first I wave went for 191 candles, and we expect the second and third I waves together to amount to 191 candles, so in theory the N wave would complete in the next 6 trading days making a swing high. If this is indeed the case, the price could reach the V target (it is almost there) or even the N target if the bulls have the necessary strength.
We do not predict the future, we can only aim to understand the current market conditions and have future expectations of when (time), how (wave), and where (price) the market will make the next turning point where one side of the market overcomes the other (bulls vs bears).
To generate this chart, we change the following settings from the default ones:
Swing length: 64
Show lines: disabled
Forecast pattern: TAITO SUCHI
Anchor forecast: 2
Show last time cycles: 5
I WAVE: enabled
N WAVE: disabled
Show last waves: 5
🔶 SETTINGS
Show Swing Highs & Lows: Enable/Disable points on swing highs and swing lows.
Swing Length: Number of candles to confirm a swing high or swing low. A higher number detects larger swings.
🔹 Ichimoku Kinkō Hyō
Show Lines: Enable/Disable the 5 Ichimoku lines: Kijun sen, Tenkan sen, Senkou span A & B and Chikou Span.
Show Kumo: Enable/Disable the Kumo (cloud). The Kumo is formed by 2 lines: Senkou Span A and Senkou Span B.
Tenkan Sen Length: Number of candles for Tenkan Sen calculation.
Kinjun Sen Length: Number of candles for the Kijun Sen calculation.
Senkou Span B Length: Number of candles for Senkou Span B calculation.
Chikou & Senkou Offset: Number of candles for Chikou and Senkou Span calculation. Chikou Span is plotted in the past, and Senkou Span A & B in the future.
🔹 Time Theory
Show Time Cycle Forecast: Enable/Disable time cycle forecast vertical lines. Disable for better performance.
Forecast Pattern: Choose between two patterns: Kihon Suchi (basic numbers) or Taito Suchi (equal numbers).
Anchor forecast on last X time cycle: Number of time cycles in the past to anchor the time cycle forecast. The larger the number, the deeper in the past the anchor will be.
Time Cycle Mode: Choose from 7 time cycle detection modes: Tenkan Sen cross, Kijun Sen cross, Kumo change between bullish & bearish, swing highs only, swing lows only, both swing highs & lows and wave detection.
Wave Cycle: Choose which type of wave to detect from 6 different wave types when the time cycle mode is set to WAVES.
Show Time Cycles: Enable/Disable time cycle horizontal lines. Disable for better performance.
how last X time cycles: Maximum number of time cycles to display.
🔹 Wave Theory
Basic Waves: Enable/Disable the display of basic waves, all at once or one at a time. Disable for better performance.
Complex Waves: Enable/Disable complex wave display, all at once or one by one. Disable for better performance.
Overlapping Waves: Enable/Disable the display of waves ending on the same swing point.
Show last X waves: 'Maximum number of waves to display.
🔹 Price Theory
Basic Targets: Enable/Disable horizontal price target lines. Disable for better performance.
Extended Targets: Enable/Disable extended price target horizontal lines. Disable for better performance.
Quinn-Fernandes Fourier Transform of Filtered Price [Loxx]Down the Rabbit Hole We Go: A Deep Dive into the Mysteries of Quinn-Fernandes Fast Fourier Transform and Hodrick-Prescott Filtering
In the ever-evolving landscape of financial markets, the ability to accurately identify and exploit underlying market patterns is of paramount importance. As market participants continuously search for innovative tools to gain an edge in their trading and investment strategies, advanced mathematical techniques, such as the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter, have emerged as powerful analytical tools. This comprehensive analysis aims to delve into the rich history and theoretical foundations of these techniques, exploring their applications in financial time series analysis, particularly in the context of a sophisticated trading indicator. Furthermore, we will critically assess the limitations and challenges associated with these transformative tools, while offering practical insights and recommendations for overcoming these hurdles to maximize their potential in the financial domain.
Our investigation will begin with a comprehensive examination of the origins and development of both the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter. We will trace their roots from classical Fourier analysis and time series smoothing to their modern-day adaptive iterations. We will elucidate the key concepts and mathematical underpinnings of these techniques and demonstrate how they are synergistically used in the context of the trading indicator under study.
As we progress, we will carefully consider the potential drawbacks and challenges associated with using the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter as integral components of a trading indicator. By providing a critical evaluation of their computational complexity, sensitivity to input parameters, assumptions about data stationarity, performance in noisy environments, and their nature as lagging indicators, we aim to offer a balanced and comprehensive understanding of these powerful analytical tools.
In conclusion, this in-depth analysis of the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter aims to provide a solid foundation for financial market participants seeking to harness the potential of these advanced techniques in their trading and investment strategies. By shedding light on their history, applications, and limitations, we hope to equip traders and investors with the knowledge and insights necessary to make informed decisions and, ultimately, achieve greater success in the highly competitive world of finance.
█ Fourier Transform and Hodrick-Prescott Filter in Financial Time Series Analysis
Financial time series analysis plays a crucial role in making informed decisions about investments and trading strategies. Among the various methods used in this domain, the Fourier Transform and the Hodrick-Prescott (HP) Filter have emerged as powerful techniques for processing and analyzing financial data. This section aims to provide a comprehensive understanding of these two methodologies, their significance in financial time series analysis, and their combined application to enhance trading strategies.
█ The Quinn-Fernandes Fourier Transform: History, Applications, and Use in Financial Time Series Analysis
The Quinn-Fernandes Fourier Transform is an advanced spectral estimation technique developed by John J. Quinn and Mauricio A. Fernandes in the early 1990s. It builds upon the classical Fourier Transform by introducing an adaptive approach that improves the identification of dominant frequencies in noisy signals. This section will explore the history of the Quinn-Fernandes Fourier Transform, its applications in various domains, and its specific use in financial time series analysis.
History of the Quinn-Fernandes Fourier Transform
The Quinn-Fernandes Fourier Transform was introduced in a 1993 paper titled "The Application of Adaptive Estimation to the Interpolation of Missing Values in Noisy Signals." In this paper, Quinn and Fernandes developed an adaptive spectral estimation algorithm to address the limitations of the classical Fourier Transform when analyzing noisy signals.
The classical Fourier Transform is a powerful mathematical tool that decomposes a function or a time series into a sum of sinusoids, making it easier to identify underlying patterns and trends. However, its performance can be negatively impacted by noise and missing data points, leading to inaccurate frequency identification.
Quinn and Fernandes sought to address these issues by developing an adaptive algorithm that could more accurately identify the dominant frequencies in a noisy signal, even when data points were missing. This adaptive algorithm, now known as the Quinn-Fernandes Fourier Transform, employs an iterative approach to refine the frequency estimates, ultimately resulting in improved spectral estimation.
Applications of the Quinn-Fernandes Fourier Transform
The Quinn-Fernandes Fourier Transform has found applications in various fields, including signal processing, telecommunications, geophysics, and biomedical engineering. Its ability to accurately identify dominant frequencies in noisy signals makes it a valuable tool for analyzing and interpreting data in these domains.
For example, in telecommunications, the Quinn-Fernandes Fourier Transform can be used to analyze the performance of communication systems and identify interference patterns. In geophysics, it can help detect and analyze seismic signals and vibrations, leading to improved understanding of geological processes. In biomedical engineering, the technique can be employed to analyze physiological signals, such as electrocardiograms, leading to more accurate diagnoses and better patient care.
Use of the Quinn-Fernandes Fourier Transform in Financial Time Series Analysis
In financial time series analysis, the Quinn-Fernandes Fourier Transform can be a powerful tool for isolating the dominant cycles and frequencies in asset price data. By more accurately identifying these critical cycles, traders can better understand the underlying dynamics of financial markets and develop more effective trading strategies.
The Quinn-Fernandes Fourier Transform is used in conjunction with the Hodrick-Prescott Filter, a technique that separates the underlying trend from the cyclical component in a time series. By first applying the Hodrick-Prescott Filter to the financial data, short-term fluctuations and noise are removed, resulting in a smoothed representation of the underlying trend. This smoothed data is then subjected to the Quinn-Fernandes Fourier Transform, allowing for more accurate identification of the dominant cycles and frequencies in the asset price data.
By employing the Quinn-Fernandes Fourier Transform in this manner, traders can gain a deeper understanding of the underlying dynamics of financial time series and develop more effective trading strategies. The enhanced knowledge of market cycles and frequencies can lead to improved risk management and ultimately, better investment performance.
The Quinn-Fernandes Fourier Transform is an advanced spectral estimation technique that has proven valuable in various domains, including financial time series analysis. Its adaptive approach to frequency identification addresses the limitations of the classical Fourier Transform when analyzing noisy signals, leading to more accurate and reliable analysis. By employing the Quinn-Fernandes Fourier Transform in financial time series analysis, traders can gain a deeper understanding of the underlying financial instrument.
Drawbacks to the Quinn-Fernandes algorithm
While the Quinn-Fernandes Fourier Transform is an effective tool for identifying dominant cycles and frequencies in financial time series, it is not without its drawbacks. Some of the limitations and challenges associated with this indicator include:
1. Computational complexity: The adaptive nature of the Quinn-Fernandes Fourier Transform requires iterative calculations, which can lead to increased computational complexity. This can be particularly challenging when analyzing large datasets or when the indicator is used in real-time trading environments.
2. Sensitivity to input parameters: The performance of the Quinn-Fernandes Fourier Transform is dependent on the choice of input parameters, such as the number of harmonic periods, frequency tolerance, and Hodrick-Prescott filter settings. Choosing inappropriate parameter values can lead to inaccurate frequency identification or reduced performance. Finding the optimal parameter settings can be challenging, and may require trial and error or a more sophisticated optimization process.
3. Assumption of stationary data: The Quinn-Fernandes Fourier Transform assumes that the underlying data is stationary, meaning that its statistical properties do not change over time. However, financial time series data is often non-stationary, with changing trends and volatility. This can limit the effectiveness of the indicator and may require additional preprocessing steps, such as detrending or differencing, to ensure the data meets the assumptions of the algorithm.
4. Limitations in noisy environments: Although the Quinn-Fernandes Fourier Transform is designed to handle noisy signals, its performance may still be negatively impacted by significant noise levels. In such cases, the identification of dominant frequencies may become less reliable, leading to suboptimal trading signals or strategies.
5. Lagging indicator: As with many technical analysis tools, the Quinn-Fernandes Fourier Transform is a lagging indicator, meaning that it is based on past data. While it can provide valuable insights into historical market dynamics, its ability to predict future price movements may be limited. This can result in false signals or late entries and exits, potentially reducing the effectiveness of trading strategies based on this indicator.
Despite these drawbacks, the Quinn-Fernandes Fourier Transform remains a valuable tool for financial time series analysis when used appropriately. By being aware of its limitations and adjusting input parameters or preprocessing steps as needed, traders can still benefit from its ability to identify dominant cycles and frequencies in financial data, and use this information to inform their trading strategies.
█ Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
1. The first term represents the deviation of the data from the trend.
2. The second term represents the smoothness of the trend.
3. λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
Another significant advantage of the HP Filter is its ability to adapt to changes in the underlying trend. This feature makes it particularly well-suited for analyzing financial time series, which often exhibit non-stationary behavior. By employing the HP Filter to smooth financial data, traders can more accurately identify and analyze the long-term trends that drive asset prices, ultimately leading to better-informed investment decisions.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
█ Combined Application of Fourier Transform and Hodrick-Prescott Filter
The integration of the Fourier Transform and the Hodrick-Prescott Filter in financial time series analysis can offer several benefits. By first applying the HP Filter to the financial data, traders can remove short-term fluctuations and noise, effectively isolating the underlying trend. This smoothed data can then be subjected to the Fourier Transform, allowing for the identification of dominant cycles and frequencies with greater precision.
By combining these two powerful techniques, traders can gain a more comprehensive understanding of the underlying dynamics of financial time series. This enhanced knowledge can lead to the development of more effective trading strategies, better risk management, and ultimately, improved investment performance.
The Fourier Transform and the Hodrick-Prescott Filter are powerful tools for financial time series analysis. Each technique offers unique benefits, with the Fourier Transform being adept at identifying dominant cycles and frequencies, and the HP Filter excelling at isolating long-term trends from short-term noise. By combining these methodologies, traders can develop a deeper understanding of the underlying dynamics of financial time series, leading to more informed investment decisions and improved trading strategies. As the financial markets continue to evolve, the combined application of these techniques will undoubtedly remain an essential aspect of modern financial analysis.
█ Features
Endpointed and Non-repainting
This is an endpointed and non-repainting indicator. These are crucial factors that contribute to its usefulness and reliability in trading and investment strategies. Let us break down these concepts and discuss why they matter in the context of a financial indicator.
1. Endpoint nature: An endpoint indicator uses the most recent data points to calculate its values, ensuring that the output is timely and reflective of the current market conditions. This is in contrast to non-endpoint indicators, which may use earlier data points in their calculations, potentially leading to less timely or less relevant results. By utilizing the most recent data available, the endpoint nature of this indicator ensures that it remains up-to-date and relevant, providing traders and investors with valuable and actionable insights into the market dynamics.
2. Non-repainting characteristic: A non-repainting indicator is one that does not change its values or signals after they have been generated. This means that once a signal or a value has been plotted on the chart, it will remain there, and future data will not affect it. This is crucial for traders and investors, as it offers a sense of consistency and certainty when making decisions based on the indicator's output.
Repainting indicators, on the other hand, can change their values or signals as new data comes in, effectively "repainting" the past. This can be problematic for several reasons:
a. Misleading results: Repainting indicators can create the illusion of a highly accurate or successful trading system when backtesting, as the indicator may adapt its past signals to fit the historical price data. This can lead to overly optimistic performance results that may not hold up in real-time trading.
b. Decision-making uncertainty: When an indicator repaints, it becomes challenging for traders and investors to trust its signals, as the signal that prompted a trade may change or disappear after the fact. This can create confusion and indecision, making it difficult to execute a consistent trading strategy.
The endpoint and non-repainting characteristics of this indicator contribute to its overall reliability and effectiveness as a tool for trading and investment decision-making. By providing timely and consistent information, this indicator helps traders and investors make well-informed decisions that are less likely to be influenced by misleading or shifting data.
Inputs
Source: This input determines the source of the price data to be used for the calculations. Users can select from options like closing price, opening price, high, low, etc., based on their preferences. Changing the source of the price data (e.g., from closing price to opening price) will alter the base data used for calculations, which may lead to different patterns and cycles being identified.
Calculation Bars: This input represents the number of past bars used for the calculation. A higher value will use more historical data for the analysis, while a lower value will focus on more recent price data. Increasing the number of past bars used for calculation will incorporate more historical data into the analysis. This may lead to a more comprehensive understanding of long-term trends but could also result in a slower response to recent price changes. Decreasing this value will focus more on recent data, potentially making the indicator more responsive to short-term fluctuations.
Harmonic Period: This input represents the harmonic period, which is the number of harmonics used in the Fourier Transform. A higher value will result in more harmonics being used, potentially capturing more complex cycles in the price data. Increasing the harmonic period will include more harmonics in the Fourier Transform, potentially capturing more complex cycles in the price data. However, this may also introduce more noise and make it harder to identify clear patterns. Decreasing this value will focus on simpler cycles and may make the analysis clearer, but it might miss out on more complex patterns.
Frequency Tolerance: This input represents the frequency tolerance, which determines how close the frequencies of the harmonics must be to be considered part of the same cycle. A higher value will allow for more variation between harmonics, while a lower value will require the frequencies to be more similar. Increasing the frequency tolerance will allow for more variation between harmonics, potentially capturing a broader range of cycles. However, this may also introduce noise and make it more difficult to identify clear patterns. Decreasing this value will require the frequencies to be more similar, potentially making the analysis clearer, but it might miss out on some cycles.
Number of Bars to Render: This input determines the number of bars to render on the chart. A higher value will result in more historical data being displayed, but it may also slow down the computation due to the increased amount of data being processed. Increasing the number of bars to render on the chart will display more historical data, providing a broader context for the analysis. However, this may also slow down the computation due to the increased amount of data being processed. Decreasing this value will speed up the computation, but it will provide less historical context for the analysis.
Smoothing Mode: This input allows the user to choose between two smoothing modes for the source price data: no smoothing or Hodrick-Prescott (HP) smoothing. The choice depends on the user's preference for how the price data should be processed before the Fourier Transform is applied. Choosing between no smoothing and Hodrick-Prescott (HP) smoothing will affect the preprocessing of the price data. Using HP smoothing will remove some of the short-term fluctuations from the data, potentially making the analysis clearer and more focused on longer-term trends. Not using smoothing will retain the original price fluctuations, which may provide more detail but also introduce noise into the analysis.
Hodrick-Prescott Filter Period: This input represents the Hodrick-Prescott filter period, which is used if the user chooses to apply HP smoothing to the price data. A higher value will result in a smoother curve, while a lower value will retain more of the original price fluctuations. Increasing the Hodrick-Prescott filter period will result in a smoother curve for the price data, emphasizing longer-term trends and minimizing short-term fluctuations. Decreasing this value will retain more of the original price fluctuations, potentially providing more detail but also introducing noise into the analysis.
Alets and signals
This indicator featues alerts, signals and bar coloring. You have to option to turn these on/off in the settings menu.
Maximum Bars Restriction
This indicator requires a large amount of processing power to render on the chart. To reduce overhead, the setting "Number of Bars to Render" is set to 500 bars. You can adjust this to you liking.
█ Related Indicators and Libraries
Goertzel Cycle Composite Wave
Goertzel Browser
Fourier Spectrometer of Price w/ Extrapolation Forecast
Fourier Extrapolator of 'Caterpillar' SSA of Price
Normalized, Variety, Fast Fourier Transform Explorer
Real-Fast Fourier Transform of Price Oscillator
Real-Fast Fourier Transform of Price w/ Linear Regression
Fourier Extrapolation of Variety Moving Averages
Fourier Extrapolator of Variety RSI w/ Bollinger Bands
Fourier Extrapolator of Price w/ Projection Forecast
Fourier Extrapolator of Price
STD-Stepped Fast Cosine Transform Moving Average
Variety RSI of Fast Discrete Cosine Transform
loxfft
TASC 2025.01 Linear Predictive Filters█ OVERVIEW
This script implements a suite of tools for identifying and utilizing dominant cycles in time series data, as introduced by John Ehlers in the "Linear Predictive Filters And Instantaneous Frequency" article featured in the January 2025 edition of TASC's Traders' Tips . Dominant cycle information can help traders adapt their indicators and strategies to changing market conditions.
█ CONCEPTS
Conventional technical indicators and strategies often rely on static, unchanging parameters, which may fail to account for the dynamic nature of market data. In his article, John Ehlers applies digital signal processing principles to address this issue, introducing linear predictive filters to identify cyclic information for adapting indicators and strategies to evolving market conditions.
This approach treats market data as a complex series in the time domain. Analyzing the series in the frequency domain reveals information about its cyclic components. To reduce the impact of frequencies outside a range of interest and focus on a specific range of cycles, Ehlers applies second-order highpass and lowpass filters to the price data, which attenuate or remove wavelengths outside the desired range. This band-limited analysis isolates specific parts of the frequency spectrum for various trading styles, e.g., longer wavelengths for position trading or shorter wavelengths for swing trading.
After filtering the series to produce band-limited data, Ehlers applies a linear predictive filter to predict future values a few bars ahead. The filter, calculated based on the techniques proposed by Lloyd Griffiths, adaptively minimizes the error between the latest data point and prediction, successively adjusting its coefficients to align with the band-limited series. The filter's coefficients can then be applied to generate an adaptive estimate of the band-limited data's structure in the frequency domain and identify the dominant cycle.
█ USAGE
This script implements the following tools presented in the article:
Griffiths Predictor
This tool calculates a linear predictive filter to forecast future data points in band-limited price data. The crosses between the prediction and signal lines can provide potential trade signals.
Griffiths Spectrum
This tool calculates a partial frequency spectrum of the band-limited price data derived from the linear predictive filter's coefficients, displaying a color-coded representation of the frequency information in the pane. This mode's display represents the data as a periodogram . The bottom of each plotted bar corresponds to a specific analyzed period (inverse of frequency), and the bar's color represents the presence of that periodic cycle in the time series relative to the one with the highest presence (i.e., the dominant cycle). Warmer, brighter colors indicate a higher presence of the cycle in the series, whereas darker colors indicate a lower presence.
Griffiths Dominant Cycle
This tool compares the cyclic components within the partial spectrum and identifies the frequency with the highest power, i.e., the dominant cycle . Traders can use this dominant cycle information to tune other indicators and strategies, which may help promote better alignment with dynamic market conditions.
Notes on parameters
Bandpass boundaries:
In the article, Ehlers recommends an upper bound of 125 bars or higher to capture longer-term cycles for position trading. He recommends an upper bound of 40 bars and a lower bound of 18 bars for swing trading. If traders use smaller lower bounds, Ehlers advises a minimum of eight bars to minimize the potential effects of aliasing.
Data length:
The Griffiths predictor can use a relatively small data length, as autocorrelation diminishes rapidly with lag. However, for optimal spectrum and dominant cycle calculations, the length must match or exceed the upper bound of the bandpass filter. Ehlers recommends avoiding excessively long lengths to maintain responsiveness to shorter-term cycles.
BAERMThe Bitcoin Auto-correlation Exchange Rate Model: A Novel Two Step Approach
THIS IS NOT FINANCIAL ADVICE. THIS ARTICLE IS FOR EDUCATIONAL AND ENTERTAINMENT PURPOSES ONLY.
If you enjoy this software and information, please consider contributing to my lightning address
Prelude
It has been previously established that the Bitcoin daily USD exchange rate series is extremely auto-correlated
In this article, we will utilise this fact to build a model for Bitcoin/USD exchange rate. But not a model for predicting the exchange rate, but rather a model to understand the fundamental reasons for the Bitcoin to have this exchange rate to begin with.
This is a model of sound money, scarcity and subjective value.
Introduction
Bitcoin, a decentralised peer to peer digital value exchange network, has experienced significant exchange rate fluctuations since its inception in 2009. In this article, we explore a two-step model that reasonably accurately captures both the fundamental drivers of Bitcoin’s value and the cyclical patterns of bull and bear markets. This model, whilst it can produce forecasts, is meant more of a way of understanding past exchange rate changes and understanding the fundamental values driving the ever increasing exchange rate. The forecasts from the model are to be considered inconclusive and speculative only.
Data preparation
To develop the BAERM, we used historical Bitcoin data from Coin Metrics, a leading provider of Bitcoin market data. The dataset includes daily USD exchange rates, block counts, and other relevant information. We pre-processed the data by performing the following steps:
Fixing date formats and setting the dataset’s time index
Generating cumulative sums for blocks and halving periods
Calculating daily rewards and total supply
Computing the log-transformed price
Step 1: Building the Base Model
To build the base model, we analysed data from the first two epochs (time periods between Bitcoin mining reward halvings) and regressed the logarithm of Bitcoin’s exchange rate on the mining reward and epoch. This base model captures the fundamental relationship between Bitcoin’s exchange rate, mining reward, and halving epoch.
where Yt represents the exchange rate at day t, Epochk is the kth epoch (for that t), and epsilont is the error term. The coefficients beta0, beta1, and beta2 are estimated using ordinary least squares regression.
Base Model Regression
We use ordinary least squares regression to estimate the coefficients for the betas in figure 2. In order to reduce the possibility of over-fitting and ensure there is sufficient out of sample for testing accuracy, the base model is only trained on the first two epochs. You will notice in the code we calculate the beta2 variable prior and call it “phaseplus”.
The code below shows the regression for the base model coefficients:
\# Run the regression
mask = df\ < 2 # we only want to use Epoch's 0 and 1 to estimate the coefficients for the base model
reg\_X = df.loc\ [mask, \ \].shift(1).iloc\
reg\_y = df.loc\ .iloc\
reg\_X = sm.add\_constant(reg\_X)
ols = sm.OLS(reg\_y, reg\_X).fit()
coefs = ols.params.values
print(coefs)
The result of this regression gives us the coefficients for the betas of the base model:
\
or in more human readable form: 0.029, 0.996869586, -0.00043. NB that for the auto-correlation/momentum beta, we did NOT round the significant figures at all. Since the momentum is so important in this model, we must use all available significant figures.
Fundamental Insights from the Base Model
Momentum effect: The term 0.997 Y suggests that the exchange rate of Bitcoin on a given day (Yi) is heavily influenced by the exchange rate on the previous day. This indicates a momentum effect, where the price of Bitcoin tends to follow its recent trend.
Momentum effect is a phenomenon observed in various financial markets, including stocks and other commodities. It implies that an asset’s price is more likely to continue moving in its current direction, either upwards or downwards, over the short term.
The momentum effect can be driven by several factors:
Behavioural biases: Investors may exhibit herding behaviour or be subject to cognitive biases such as confirmation bias, which could lead them to buy or sell assets based on recent trends, reinforcing the momentum.
Positive feedback loops: As more investors notice a trend and act on it, the trend may gain even more traction, leading to a self-reinforcing positive feedback loop. This can cause prices to continue moving in the same direction, further amplifying the momentum effect.
Technical analysis: Many traders use technical analysis to make investment decisions, which often involves studying historical exchange rate trends and chart patterns to predict future exchange rate movements. When a large number of traders follow similar strategies, their collective actions can create and reinforce exchange rate momentum.
Impact of halving events: In the Bitcoin network, new bitcoins are created as a reward to miners for validating transactions and adding new blocks to the blockchain. This reward is called the block reward, and it is halved approximately every four years, or every 210,000 blocks. This event is known as a halving.
The primary purpose of halving events is to control the supply of new bitcoins entering the market, ultimately leading to a capped supply of 21 million bitcoins. As the block reward decreases, the rate at which new bitcoins are created slows down, and this can have significant implications for the price of Bitcoin.
The term -0.0004*(50/(2^epochk) — (epochk+1)²) accounts for the impact of the halving events on the Bitcoin exchange rate. The model seems to suggest that the exchange rate of Bitcoin is influenced by a function of the number of halving events that have occurred.
Exponential decay and the decreasing impact of the halvings: The first part of this term, 50/(2^epochk), indicates that the impact of each subsequent halving event decays exponentially, implying that the influence of halving events on the Bitcoin exchange rate diminishes over time. This might be due to the decreasing marginal effect of each halving event on the overall Bitcoin supply as the block reward gets smaller and smaller.
This is antithetical to the wrong and popular stock to flow model, which suggests the opposite. Given the accuracy of the BAERM, this is yet another reason to question the S2F model, from a fundamental perspective.
The second part of the term, (epochk+1)², introduces a non-linear relationship between the halving events and the exchange rate. This non-linear aspect could reflect that the impact of halving events is not constant over time and may be influenced by various factors such as market dynamics, speculation, and changing market conditions.
The combination of these two terms is expressed by the graph of the model line (see figure 3), where it can be seen the step from each halving is decaying, and the step up from each halving event is given by a parabolic curve.
NB - The base model has been trained on the first two halving epochs and then seeded (i.e. the first lag point) with the oldest data available.
Constant term: The constant term 0.03 in the equation represents an inherent baseline level of growth in the Bitcoin exchange rate.
In any linear or linear-like model, the constant term, also known as the intercept or bias, represents the value of the dependent variable (in this case, the log-scaled Bitcoin USD exchange rate) when all the independent variables are set to zero.
The constant term indicates that even without considering the effects of the previous day’s exchange rate or halving events, there is a baseline growth in the exchange rate of Bitcoin. This baseline growth could be due to factors such as the network’s overall growth or increasing adoption, or changes in the market structure (more exchanges, changes to the regulatory environment, improved liquidity, more fiat on-ramps etc).
Base Model Regression Diagnostics
Below is a summary of the model generated by the OLS function
OLS Regression Results
\==============================================================================
Dep. Variable: logprice R-squared: 0.999
Model: OLS Adj. R-squared: 0.999
Method: Least Squares F-statistic: 2.041e+06
Date: Fri, 28 Apr 2023 Prob (F-statistic): 0.00
Time: 11:06:58 Log-Likelihood: 3001.6
No. Observations: 2182 AIC: -5997.
Df Residuals: 2179 BIC: -5980.
Df Model: 2
Covariance Type: nonrobust
\==============================================================================
coef std err t P>|t| \
\------------------------------------------------------------------------------
const 0.0292 0.009 3.081 0.002 0.011 0.048
logprice 0.9969 0.001 1012.724 0.000 0.995 0.999
phaseplus -0.0004 0.000 -2.239 0.025 -0.001 -5.3e-05
\==============================================================================
Omnibus: 674.771 Durbin-Watson: 1.901
Prob(Omnibus): 0.000 Jarque-Bera (JB): 24937.353
Skew: -0.765 Prob(JB): 0.00
Kurtosis: 19.491 Cond. No. 255.
\==============================================================================
Below we see some regression diagnostics along with the regression itself.
Diagnostics: We can see that the residuals are looking a little skewed and there is some heteroskedasticity within the residuals. The coefficient of determination, or r2 is very high, but that is to be expected given the momentum term. A better r2 is manually calculated by the sum square of the difference of the model to the untrained data. This can be achieved by the following code:
\# Calculate the out-of-sample R-squared
oos\_mask = df\ >= 2
oos\_actual = df.loc\
oos\_predicted = df.loc\
residuals\_oos = oos\_actual - oos\_predicted
SSR = np.sum(residuals\_oos \*\* 2)
SST = np.sum((oos\_actual - oos\_actual.mean()) \*\* 2)
R2\_oos = 1 - SSR/SST
print("Out-of-sample R-squared:", R2\_oos)
The result is: 0.84, which indicates a very close fit to the out of sample data for the base model, which goes some way to proving our fundamental assumption around subjective value and sound money to be accurate.
Step 2: Adding the Damping Function
Next, we incorporated a damping function to capture the cyclical nature of bull and bear markets. The optimal parameters for the damping function were determined by regressing on the residuals from the base model. The damping function enhances the model’s ability to identify and predict bull and bear cycles in the Bitcoin market. The addition of the damping function to the base model is expressed as the full model equation.
This brings me to the question — why? Why add the damping function to the base model, which is arguably already performing extremely well out of sample and providing valuable insights into the exchange rate movements of Bitcoin.
Fundamental reasoning behind the addition of a damping function:
Subjective Theory of Value: The cyclical component of the damping function, represented by the cosine function, can be thought of as capturing the periodic fluctuations in market sentiment. These fluctuations may arise from various factors, such as changes in investor risk appetite, macroeconomic conditions, or technological advancements. Mathematically, the cyclical component represents the frequency of these fluctuations, while the phase shift (α and β) allows for adjustments in the alignment of these cycles with historical data. This flexibility enables the damping function to account for the heterogeneity in market participants’ preferences and expectations, which is a key aspect of the subjective theory of value.
Time Preference and Market Cycles: The exponential decay component of the damping function, represented by the term e^(-0.0004t), can be linked to the concept of time preference and its impact on market dynamics. In financial markets, the discounting of future cash flows is a common practice, reflecting the time value of money and the inherent uncertainty of future events. The exponential decay in the damping function serves a similar purpose, diminishing the influence of past market cycles as time progresses. This decay term introduces a time-dependent weight to the cyclical component, capturing the dynamic nature of the Bitcoin market and the changing relevance of past events.
Interactions between Cyclical and Exponential Decay Components: The interplay between the cyclical and exponential decay components in the damping function captures the complex dynamics of the Bitcoin market. The damping function effectively models the attenuation of past cycles while also accounting for their periodic nature. This allows the model to adapt to changing market conditions and to provide accurate predictions even in the face of significant volatility or structural shifts.
Now we have the fundamental reasoning for the addition of the function, we can explore the actual implementation and look to other analogies for guidance —
Financial and physical analogies to the damping function:
Mathematical Aspects: The exponential decay component, e^(-0.0004t), attenuates the amplitude of the cyclical component over time. This attenuation factor is crucial in modelling the diminishing influence of past market cycles. The cyclical component, represented by the cosine function, accounts for the periodic nature of market cycles, with α determining the frequency of these cycles and β representing the phase shift. The constant term (+3) ensures that the function remains positive, which is important for practical applications, as the damping function is added to the rest of the model to obtain the final predictions.
Analogies to Existing Damping Functions: The damping function in the BAERM is similar to damped harmonic oscillators found in physics. In a damped harmonic oscillator, an object in motion experiences a restoring force proportional to its displacement from equilibrium and a damping force proportional to its velocity. The equation of motion for a damped harmonic oscillator is:
x’’(t) + 2γx’(t) + ω₀²x(t) = 0
where x(t) is the displacement, ω₀ is the natural frequency, and γ is the damping coefficient. The damping function in the BAERM shares similarities with the solution to this equation, which is typically a product of an exponential decay term and a sinusoidal term. The exponential decay term in the BAERM captures the attenuation of past market cycles, while the cosine term represents the periodic nature of these cycles.
Comparisons with Financial Models: In finance, damped oscillatory models have been applied to model interest rates, stock prices, and exchange rates. The famous Black-Scholes option pricing model, for instance, assumes that stock prices follow a geometric Brownian motion, which can exhibit oscillatory behavior under certain conditions. In fixed income markets, the Cox-Ingersoll-Ross (CIR) model for interest rates also incorporates mean reversion and stochastic volatility, leading to damped oscillatory dynamics.
By drawing on these analogies, we can better understand the technical aspects of the damping function in the BAERM and appreciate its effectiveness in modelling the complex dynamics of the Bitcoin market. The damping function captures both the periodic nature of market cycles and the attenuation of past events’ influence.
Conclusion
In this article, we explored the Bitcoin Auto-correlation Exchange Rate Model (BAERM), a novel 2-step linear regression model for understanding the Bitcoin USD exchange rate. We discussed the model’s components, their interpretations, and the fundamental insights they provide about Bitcoin exchange rate dynamics.
The BAERM’s ability to capture the fundamental properties of Bitcoin is particularly interesting. The framework underlying the model emphasises the importance of individuals’ subjective valuations and preferences in determining prices. The momentum term, which accounts for auto-correlation, is a testament to this idea, as it shows that historical price trends influence market participants’ expectations and valuations. This observation is consistent with the notion that the price of Bitcoin is determined by individuals’ preferences based on past information.
Furthermore, the BAERM incorporates the impact of Bitcoin’s supply dynamics on its price through the halving epoch terms. By acknowledging the significance of supply-side factors, the model reflects the principles of sound money. A limited supply of money, such as that of Bitcoin, maintains its value and purchasing power over time. The halving events, which reduce the block reward, play a crucial role in making Bitcoin increasingly scarce, thus reinforcing its attractiveness as a store of value and a medium of exchange.
The constant term in the model serves as the baseline for the model’s predictions and can be interpreted as an inherent value attributed to Bitcoin. This value emphasizes the significance of the underlying technology, network effects, and Bitcoin’s role as a medium of exchange, store of value, and unit of account. These aspects are all essential for a sound form of money, and the model’s ability to account for them further showcases its strength in capturing the fundamental properties of Bitcoin.
The BAERM offers a potential robust and well-founded methodology for understanding the Bitcoin USD exchange rate, taking into account the key factors that drive it from both supply and demand perspectives.
In conclusion, the Bitcoin Auto-correlation Exchange Rate Model provides a comprehensive fundamentally grounded and hopefully useful framework for understanding the Bitcoin USD exchange rate.
RSI3M3+ v.1.8RSI3M3+ v.1.8 Indicator
This script is an advanced trading indicator based on Walter J. Bressert's cycle analysis methodology, combined with an RSI (Relative Strength Index) variation. Let me break it down and explain how it works.
Core Concepts
The RSI3M3+ indicator combines:
A short-term RSI (3-period)
A 3-period moving average to smooth the RSI
Bressert's cycle analysis principles to identify optimal trading points
RSI3M3+ Indicator VisualizationImage Walter J. Bressert's Cycle Analysis Concepts
Walter Bressert was a pioneer in cycle analysis trading who believed markets move in cyclical patterns that can be measured and predicted. His key principles integrated into this indicator include:
Trading Cycles: Markets move in cycles with measurable time spans from low to low
Timing Bands: Projected periods when the next cyclical low or high is anticipated
Oscillator Use: Using oscillators like RSI to confirm cycle position
Entry/Exit Rules: Specific rules for trade entry and exit based on cycle position
Key Parameters in the Script
Basic RSI Parameters
Required bars: Minimum number of bars needed (default: 20)
Overbought region: RSI level considered overbought (default: 70)
Oversold region: RSI level considered oversold (default: 30)
Bressert-Specific Parameters
Cycle Detection Length: Lookback period for cycle identification (default: 30)
Minimum/Maximum Cycle Length: Expected cycle duration in days (default: 15-30)
Buy Line: Lower threshold for buy signals (default: 40)
Sell Line: Upper threshold for sell signals (default: 60)
How the Indicator Works
RSI3M3 Calculation:
Calculates a 3-period RSI (sRSI)
Smooths it with a 3-period moving average (sMA)
Cycle Detection:
Identifies bottoms: When the RSI is below the buy line (40) and starting to turn up
Identifies tops: When the RSI is above the sell line (60) and starting to turn down
Records these points to calculate cycle lengths
Timing Bands:
Projects when the next cycle bottom or top should occur
Creates visual bands on the chart showing these expected time windows
Signal Generation:
Buy signals occur when the RSI turns up from below the oversold level (30)
Sell signals occur when the RSI turns down from above the overbought level (70)
Enhanced by Bressert's specific timing rules
Bressert's Five Trading Rules (Implemented in the Script)
Cycle Timing: The low must be 15-30 market days from the previous Trading Cycle bottom
Prior Top Validation: A Trading Cycle high must have occurred with the oscillator above 60
Oscillator Behavior: The oscillator must drop below 40 and turn up
Entry Trigger: Entry is triggered by a rise above the price high of the upturn day
Protective Stop: Place stop slightly below the Trading Cycle low (implemented as 99% of bottom price)
How to Use the Indicator
Reading the Chart
Main Plot Area:
Green line: 3-period RSI
Red line: 3-period moving average of the RSI
Horizontal bands: Oversold (30) and Overbought (70) regions
Dotted lines: Buy line (40) and Sell line (60)
Yellow vertical bands: Projected timing windows for next cycle bottom
Signals:
Green up arrows: Buy signals
Red down arrows: Sell signals
Trading Strategy
For Buy Signals:
Wait for the RSI to drop below the buy line (40)
Look for an upturn in the RSI from below this level
Enter the trade when price rises above the high of the upturn day
Place a protective stop at 99% of the Trading Cycle low
For Sell Signals:
Wait for the RSI to rise above the sell line (60)
Look for a downturn in the RSI from above this level
Consider exiting or taking profits when a sell signal appears
Alternative exit: When price moves below the low of the downturn day
Cycle Timing Enhancement:
Pay attention to the yellow timing bands
Signals occurring within these bands have higher probability of success
Signals outside these bands may be less reliable
Practical Tips for Using RSI3M3+
Timeframe Selection:
The indicator works best on daily charts for intermediate-term trading
Can be used on weekly charts for longer-term position trading
On intraday charts, adjust cycle lengths accordingly
Market Applicability:
Works well in trending markets with clear cyclical behavior
Less effective in choppy, non-trending markets
Consider additional indicators for trend confirmation
Parameter Adjustment:
Different markets may have different natural cycle lengths
You may need to adjust the min/max cycle length parameters
Higher volatility markets may need wider overbought/oversold levels
Trade Management:
Enter trades when all Bressert's conditions are met
Use the protective stop as defined (99% of cycle low)
Consider taking partial profits at the projected cycle high timing
Advanced Techniques
Multiple Timeframe Analysis:
Confirm signals with the same indicator on higher timeframes
Enter in the direction of the larger cycle when smaller and larger cycles align
Divergence Detection:
Look for price making new lows while RSI makes higher lows (bullish)
Look for price making new highs while RSI makes lower highs (bearish)
Confluence with Price Action:
Combine with support/resistance levels
Use with candlestick patterns for confirmation
Consider volume confirmation of cycle turns
This RSI3M3+ indicator combines the responsiveness of a short-term RSI with the predictive power of Bressert's cycle analysis, offering traders a sophisticated tool for identifying high-probability trading opportunities based on market cycles and momentum shifts.
THANK YOU FOR PREVIOUS CODER THAT EFFORT TO CREATE THE EARLIER VERSION THAT MAKE WALTER J BRESSERT CONCEPT IN TRADINGVIEW @ADutchTourist
Quarterly Theory ICT 04 [TradingFinder] SSMT 4Quarter Divergence🔵 Introduction
Sequential SMT Divergence is an advanced price-action-based analytical technique rooted in the ICT (Inner Circle Trader) methodology. Its primary objective is to identify early-stage divergences between correlated assets within precise time structures. This tool not only breaks down market structure but also enables traders to detect engineered liquidity traps before the market reacts.
In simple terms, SMT (Smart Money Technique) occurs when two correlated assets—such as indices (ES and NQ), currency pairs (EURUSD and GBPUSD), or commodities (Gold and Silver)—exhibit different reactions at key price levels (swing highs or lows). This lack of alignment is often a sign of smart money manipulation and signals a lack of confirmation in the ongoing trend—hinting at an imminent reversal or at least a pause in momentum.
In its Sequential form, SMT divergences are examined through a more granular temporal lens—between intraday quarters (Q1 through Q4). When SMT appears at the transition from one quarter to another (e.g., Q1 to Q2 or Q3 to Q4), the signal becomes significantly more powerful, often aligning with a critical phase in the Quarterly Theory—a framework that segments market behavior into four distinct phases: Accumulation, Manipulation, Distribution, and Reversal/Continuation.
For instance, a Bullish SMT forms when one asset prints a new low while its correlated counterpart fails to break the corresponding low from the previous quarter. This usually indicates absorption of selling pressure and the beginning of accumulation by smart money. Conversely, a Bearish SMT arises when one asset makes a higher high, but the second asset fails to confirm, signaling distribution or a fake-out before a decline.
However, SMT alone is not enough. To confirm a true Market Structure Break (MSB), the appearance of a Precision Swing Point (PSP) is essential—a specific candlestick formation on a lower timeframe (typically 5 to 15 minutes) that reveals the entry of institutional participants. The combination of SMT and PSP provides a more accurate entry point and better understanding of premium and discount zones.
The Sequential SMT Indicator, introduced in this article, dynamically scans charts for such divergence patterns across multiple sessions. It is applicable to various markets including Forex, crypto, commodities, and indices, and shows particularly strong performance during mid-week sessions (Wednesdays and Thursdays)—when most weekly highs and lows tend to form.
Bullish Sequential SMT :
Bearish Sequential SMT :
🔵 How to Use
The Sequential SMT (SSMT) indicator is designed to detect time and structure-based divergences between two correlated assets. This divergence occurs when both assets print a similar swing (high or low) in the previous quarter (e.g., Q3), but in the current quarter (e.g., Q4), only one asset manages to break that swing level—while the other fails to reach it.
This temporal mismatch is precisely identified by the SSMT indicator and often signals smart money activity, a market phase transition, or even the presence of an engineered liquidity trap. The signal becomes especially powerful when paired with a Precision Swing Point (PSP)—a confirming candle on lower timeframes (5m–15m) that typically indicates a market structure break (MSB) and the entry of smart liquidity.
🟣 Bullish Sequential SMT
In the previous quarter, both assets form a similar swing low.
In the current quarter, one asset (e.g., EURUSD) breaks that low and trades below it.
The other asset (e.g., GBPUSD) fails to reach the same low, preserving the structure.
This time-based divergence reflects declining selling pressure, potential absorption, and often marks the end of a manipulation phase and the start of accumulation. If confirmed by a bullish PSP candle, it offers a strong long opportunity, with stop-losses defined just below the swing low.
🟣 Bearish Sequential SMT
In the previous quarter, both assets form a similar swing high.
In the current quarter, one asset (e.g., NQ) breaks above that high.
The other asset (e.g., ES) fails to reach that high, remaining below it.
This type of divergence signals weakening bullish momentum and the likelihood of distribution or a fake-out before a price drop. When followed by a bearish PSP candle, it sets up a strong shorting opportunity with targets in the discount zone and protective stops placed above the swing high.
🔵 Settings
⚙️ Logical Settings
Quarterly Cycles Type : Select the time segmentation method for SMT analysis.
Available modes include: Yearly, Monthly, Weekly, Daily, 90 Minute, and Micro.
These define how the indicator divides market time into Q1–Q4 cycles.
Symbol : Choose the secondary asset to compare with the main chart asset (e.g., XAUUSD, US100, GBPUSD).
Pivot Period : Sets the sensitivity of the pivot detection algorithm. A smaller value increases responsiveness to price swings.
Activate Max Pivot Back : When enabled, limits the maximum number of past pivots to be considered for divergence detection.
Max Pivot Back Length : Defines how many past pivots can be used (if the above toggle is active).
Pivot Sync Threshold : The maximum allowed difference (in bars) between pivots of the two assets for them to be compared.
Validity Pivot Length : Defines the time window (in bars) during which a divergence remains valid before it's considered outdated.
🎨 Display Settings
Show Cycle :Toggles the visual display of the current Quarter (Q1 to Q4) based on the selected time segmentation
Show Cycle Label : Shows the name (e.g., "Q2") of each detected Quarter on the chart.
Show Bullish SMT Line : Draws a line connecting the bullish divergence points.
Show Bullish SMT Label : Displays a label on the chart when a bullish divergence is detected.
Bullish Color : Sets the color for bullish SMT markers (label, shape, and line).
Show Bearish SMT Line : Draws a line for bearish divergence.
Show Bearish SMT Label : Displays a label when a bearish SMT divergence is found.
Bearish Color : Sets the color for bearish SMT visual elements.
🔔 Alert Settings
Alert Name : Custom name for the alert messages (used in TradingView’s alert system).
Message Frequency :
All: Every signal triggers an alert.
Once Per Bar: Alerts once per bar regardless of how many signals occur.
Per Bar Close: Only triggers when the bar closes and the signal still exists.
Time Zone Display : Choose the time zone in which alert timestamps are displayed (e.g., UTC).
Bullish SMT Divergence Alert : Enable/disable alerts specifically for bullish signals.
Bearish SMT Divergence Alert : Enable/disable alerts specifically for bearish signals
🔵 Conclusion
The Sequential SMT (SSMT) indicator is a powerful and precise tool for identifying structural divergences between correlated assets within a time-based framework. Unlike traditional divergence models that rely solely on sequential pivot comparisons, SSMT leverages Quarterly Theory, in combination with concepts like liquidity sweeps, market structure breaks (MSB) and precision swing points (PSP), to provide a deeper and more actionable view of market dynamics.
By using SSMT, traders gain not only the ability to identify where divergence occurs, but also when it matters most within the market cycle. This empowers them to anticipate major moves or traps before they fully materialize, and position themselves accordingly in high-probability trade zones.
Whether you're trading Forex, crypto, indices, or commodities, the true strength of this indicator is revealed when used in sync with the Accumulation, Manipulation, Distribution, and Reversal phases of the market. Integrated with other confluence tools and market models, SSMT can serve as a core component in a professional, rule-based, and highly personalized trading strategy.
Hurst Future Lines of Demarcation StrategyJ. M. Hurst introduced a concept in technical analysis known as the Future Line of Demarcation (FLD), which serves as a forward-looking tool by incorporating a simple yet profound line into future projections on a financial chart. Specifically, the FLD is constructed by offsetting the price half a cycle ahead into the future on the time axis, relative to the Hurst Cycle of interest. For instance, in the context of a 40 Day Cycle, the FLD would be represented by shifting the current price data 20 days forward on the chart, offering an idea of future price movement anticipations.
The utility of FLDs extends into three critical areas of insight, which form the backbone of the FLD Trading Strategy:
A price crossing the FLD signifies the confirmation of either a peak or trough formation, indicating pivotal moments in price action.
Such crossings also help determine precise price targets for the upcoming peak or trough, aligned with the cycle of examination.
Additionally, the occurrence of a peak in the FLD itself signals a probable zone where the price might experience a trough, helping to anticipate of future price movements.
These insights by Hurst in his "Cycles Trading Course" during the 1970s, are instrumental for traders aiming to determine entry and exit points, and to forecast potential price movements within the market.
To use the FLD Trading Strategy, for example when focusing on the 40 Day Cycle, a trader should primarily concentrate on the interplay between three Hurst Cycles:
The 20 Day FLD (Signal) - Half the length of the Trade Cycle
The 40 Day FLD (Trade) - The Cycle you want to trade
The 80 Day FLD (Trend) - Twice the length of the Trade Cycle
Traders can gauge trend or consolidation by watching for two critical patterns:
Cascading patterns, characterized by several FLDs running parallel with a consistent separation, typically emerge during pronounced market trends, indicating strong directional momentum.
Consolidation patterns, on the other hand, occur when multiple FLDs intersect and navigate within the same price bandwidth, often reversing direction to traverse this range multiple times. This tangled scenario results in the formation of Pause Zones, areas where price momentum is likely to temporarily stall or where the emergence of a significant trend might be delayed.
This simple FLD indicator provides 3 FLDs with optional source input and smoothing, A-through-H FLD interaction background, adjustable “Close the Trade” triggers, and a simple strategy for backtesting it all.
The A-through-H FLD interactions are a framework designed to classify the different types of price movements as they intersect with or diverge from the Future Line of Demarcation (FLD). Each interaction (designated A through H by color) represents a specific phase or characteristic within the cycle, and understanding these can help traders anticipate future price movements and make informed decisions.
The adjustable “Close the Trade” triggers are for setting the crossover/under that determines the trade exits. The options include: Price, Signal FLD, Trade FLD, or Trend FLD. For example, a trader may want to exit trades only when price finally crosses the Trade FLD line.
Shoutouts & Credits for all the raw code, helpful information, ideas & collaboration, conversations together, introductions, indicator feedback, and genuine/selfless help:
🏆 @TerryPascoe
🏅 @Hpotter
👏 @parisboy
