PAS/ML Hybrid Score System Metrics & SignalsThis tool provides trade signal visualization and live performance metrics for the PAS+ML Hybrid framework. It builds on the core " Price Action Strength/Machine Learning Hybrid Score System " indicator and displays actionable entries, exits, and historical trade statistics directly on the chart.
Signals:
Plots entry (▲) and exit (▼) arrows based on the Hybrid PAS+ML crossover logic, with an optional long-term trend filter for confirmation. Entry arrows occur at candle following the signal (i.e. the next open); exit arrows occur on the same candle, at the close. Metrics are calculated using these prices.
Performance Metrics:
Displays a live table of cumulative results including total trades, win rate, average realized profit, average maximum profit, and profit after X bars. Results can be viewed in percent or pips.
Customization:
Adjustable parameters for lookback lengths, smoothing, ML weighting, trend filter type (SMA/EMA), and FX pip display options.
Integration:
Designed to be used together with the ""Price Action Strength/Machine Learning Hybrid Score System" indicator, which provides the underlying hybrid score and volatility context. Use this metrics version for trade execution analysis and performance tracking.
Use Case:
Ideal for traders who want to quantify the historical and ongoing effectiveness of PAS+ML hybrid signals. Can assist in refining thresholds, holding periods, and risk-reward calibration.
Doğrusal Regresyon
Price Action Strength/Machine Learning Hybrid Score SystemThis indicator combines Price Action Strength (PAS) with a Machine Learning (ML) derived signal to form a dynamic hybrid momentum model. It helps visualize underlying trend quality and predictive strength, and includes optional Bollinger Bands for volatility context.
PAS (Price Action Strength):
Measures directional momentum using the slope of a linear regression and candle body bias. The slope can be normalized by ATR or price and is smoothed using EMAs for stability.
ML Score:
Computes a predictive signal using multiple technical features (such as distance from recent highs/lows, EMA change, SMA slope, and MACD histogram). The result is z-scored and smoothed via WMA for noise reduction.
Hybrid Score:
Dynamically weights PAS and ML signals. PAS dominates when ML confidence is low; ML influence increases as predictive strength rises. Produces a smooth, normalized hybrid curve oscillating around zero.
Bollinger Bands (optional):
Can be plotted on the ML smooth line, PAS normalized line, or Hybrid Score (selectable). Configurable length and multiplier to visualize volatility and overbought/oversold zones.
Visualization:
- PAS (blue), ML (orange), and Hybrid (aqua) plotted together.
- Background shading indicates bullish (green) or bearish (red) hybrid momentum.
- Optional Bollinger Bands for visual reference.
Inputs:
- PAS length, smoothing, and signal EMA
- ATR normalization toggle
- ML toggle, smoothing, and weighting scale
- Bollinger Bands toggle, source, length, and multiplier
Usage:
- Hybrid Score above zero suggests bullish momentum
- Hybrid Score below zero suggests bearish momentum
- Bollinger Band extremes can highlight potential turning points
- Better results on higher timeframes (i.e. 1H+)
Companion Indicator:
This indicator pairs with "PAS/ML Hybrid Score System Metrics & Signals " , a separate tool that displays trade signals and performance metrics directly on the price chart. Use both together for a full analytical workflow.
ML-Enhanced Multi-Indicator Composite Signal🤖 ML-Enhanced Multi-Indicator Composite Signal
Revolutionary AI-Powered Trading Indicator with Adaptive Learning
Transform your trading with cutting-edge machine learning technology that automatically optimizes indicator weights based on real market performance!
🎯 What Makes This Indicator Special?
This isn't just another composite indicator. It's an intelligent trading system that learns from market data and continuously adapts to improve signal accuracy. Unlike static indicators with fixed weights, this AI-powered tool dynamically adjusts the importance of each technical indicator based on their actual prediction success rates.
⚡ Key Features
🤖 Adaptive Machine Learning Engine
Automatically tracks prediction accuracy for each indicator
Dynamically adjusts weights based on performance
Continuous learning and adaptation to market conditions
Configurable learning parameters for fine-tuning
📊 Multi-Indicator Fusion
SuperTrend: Trend direction and momentum
Moving Averages: Price trend confirmation (SMA/EMA/WMA/RMA)
VWAP: Volume-weighted price levels
Linear Regression: Mathematical trend analysis
🎯 Intelligent Signal Generation
Strong Buy/Buy/Sell/Strong Sell signals
Configurable threshold levels
Signal smoothing to reduce noise
Smart signal timing to avoid repetitive alerts
📈 Performance Analytics Dashboard
Real-time accuracy tracking for each indicator
Weight distribution visualization
ML vs. Equal weights comparison
Learning progress monitoring
🚀 How It Works
1. Data Collection Phase
The indicator continuously monitors the performance of each technical component, storing predictions and actual market outcomes.
2. Learning Phase
Using configurable learning periods (20-500 bars), the ML engine calculates accuracy rates for each indicator's predictions.
3. Weight Optimization
Based on performance data, the system automatically adjusts weights using a configurable learning rate, ensuring better-performing indicators have more influence.
4. Signal Generation
The optimized composite signal triggers buy/sell alerts when crossing predefined thresholds, with visual signals and background coloring.
⚙️ Customization Options
Machine Learning Parameters
Learning Period: 20-500 bars (default: 100)
Prediction Horizon: 1-20 bars (default: 5)
Learning Rate: 0.01-1.0 (default: 0.1)
Minimum Weight: Prevents any indicator from becoming irrelevant
Performance Smoothing: Reduces noise in accuracy calculations
Traditional Settings
SuperTrend: Period and multiplier adjustment
Moving Average: Type selection and length
VWAP: Source customization
Linear Regression: Length and source options
Signal Configuration
Threshold Levels: Customizable buy/sell trigger points
Signal Smoothing: Reduces false signals
Manual Override: Option to use fixed weights instead of ML
📱 Visual Features
Signal Line Display
Dynamic color coding based on signal strength
Threshold level lines for clear entry/exit points
Background coloring for quick market sentiment assessment
Performance Table
Real-time accuracy metrics for each indicator
Current weight distribution showing ML optimization
Performance comparison between ML and equal weights
Learning progress indicator
Signal Shapes
🚀 Strong Buy: Large green triangle with text
📈 Buy: Standard green triangle
📉 Sell: Standard red triangle
💥 Strong Sell: Large red triangle with text
🎓 Best Practices & Usage Tips
For Beginners
Start with default ML settings
Allow 100+ bars for proper learning
Focus on Strong Buy/Sell signals initially
Monitor the performance table to understand ML adaptation
For Advanced Traders
Adjust learning rate based on market volatility
Customize prediction horizon for your trading timeframe
Fine-tune threshold levels for your risk tolerance
Combine with additional confirmation indicators
Recommended Settings by Timeframe
Scalping (1m-5m): Learning Period: 50, Prediction Horizon: 3
Day Trading (15m-1h): Learning Period: 100, Prediction Horizon: 5
Swing Trading (4h-1D): Learning Period: 200, Prediction Horizon: 10
🔔 Alert System
Set up comprehensive alerts for:
Strong Buy/Sell signals with maximum consensus
Regular Buy/Sell signals for standard entries
Custom message templates with price and signal strength
Email, SMS, and webhook compatibility
⚠️ Important Notes
Learning Period: Allow sufficient data for ML optimization (minimum 50 bars recommended)
Market Conditions: Performance may vary during high volatility or trending vs. ranging markets
Backtesting: Test thoroughly on historical data before live trading
Risk Management: Always use proper position sizing and stop losses
🏆 Why Choose This Indicator?
✅ Adaptive Intelligence: Unlike static indicators, this tool evolves with market conditions
✅ Transparent Performance: See exactly how well each component is performing
✅ Comprehensive Analytics: Make informed decisions with detailed performance metrics
✅ Professional Grade: Developed by experienced traders for serious market participants
✅ Continuous Innovation: Regular updates and improvements based on user feedback
📊 Performance Tracking
The indicator provides unprecedented transparency into its decision-making process:
Individual indicator accuracy rates
Weight evolution over time
Improvement metrics vs. baseline
Learning curve visualization
Transform your trading with the power of adaptive machine learning. Let the market data guide your strategy optimization automatically!
Tags: Machine Learning, AI Trading, Composite Signal, Multi-Indicator, Adaptive Algorithm, Signal Generation, Trading Automation, Technical Analysis
Category: Trend Following, Oscillators, Signal Generators
StockAlgo | Alpha v1.1Stock Algo Alpha provides Buy Sell indicators along with automated trading ability.
AI Dynamic SR Trend Lines Enhanced# Dynamic Support/Resistance Lines Using Linear Regression
## What Makes This Script Original
This script differs from standard pivot-based support/resistance indicators by applying **linear regression analysis** to clusters of recent pivot points instead of simply connecting the last two pivots. While many scripts plot lines between individual swing points, this approach calculates the "line of best fit" through multiple recent pivots (3-5 points), creating statistically-derived trend lines that better represent the overall price trajectory.
## Core Methodology
**Pivot Collection & Filtering:**
- Detects swing highs and lows using configurable left/right lookback periods
- Applies ATR-based filtering to exclude minor pivots that don't represent significant price structure
- Uses angular filtering to reject excessively steep trend lines (over 45 degrees by default)
**Linear Regression Calculation:**
- Collects the most recent 2-5 valid pivot points (user configurable)
- Applies least-squares linear regression to find the optimal line through these points
- Updates dynamically as new pivots form, maintaining relevance to current market structure
**Enhancement Features:**
- Optional logarithmic price scaling for percentage-based analysis
- EMA confluence detection that increases line "strength" when trend lines align with moving averages
- Automatic line pruning when price moves significantly away (customizable ATR multiples)
- Visual strength indication through line thickness based on pivot count and confluence
## Key Differences from Standard Approaches
**vs. Simple Pivot Connections:** Uses statistical best-fit rather than arbitrary point-to-point lines
**vs. Fixed Trend Lines:** Dynamically adapts as new market structure develops
**vs. Manual Drawing:** Automatically identifies and plots the most statistically relevant levels
## Practical Application
The resulting support and resistance lines represent the mathematical trend through recent price structure rather than subjective line drawing. This creates more consistent and objective trend analysis, particularly useful for:
- Identifying key levels for entries/exits
- Confluence analysis when combined with other technical tools
- Systematic approach to trend line analysis
## Important Limitations
- Lines recalculate as new pivots form (this is intentional for dynamic adaptation)
- Requires sufficient pivot history to generate meaningful regression lines
- Should be used as part of comprehensive analysis, not as standalone signals
- Past performance of trend lines does not guarantee future effectiveness
## Technical Implementation Notes
The script uses arrays to maintain rolling collections of pivot points, applies mathematical linear regression formulas, and includes multiple filtering mechanisms to ensure only statistically significant levels are displayed. All visual elements and calculation parameters are fully customizable to suit different trading styles and timeframes.
Squeeze Momentum Regression Clouds [SciQua]╭──────────────────────────────────────────────╮
☁️ Squeeze Momentum Regression Clouds
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🔍 Overview
The Squeeze Momentum Regression Clouds (SMRC) indicator is a powerful visual tool for identifying price compression , trend strength , and slope momentum using multiple layers of linear regression Clouds. Designed to extend the classic squeeze framework, this indicator captures the behavior of price through dynamic slope detection, percentile-based spread analytics, and an optional UI for trend inspection — across up to four customizable regression Clouds .
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⚙️ Core Features
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Up to 4 Regression Clouds – Each Cloud is created from a top and bottom linear regression line over a configurable lookback window.
Slope Detection Engine – Identifies whether each band is rising, falling, or flat based on slope-to-ATR thresholds.
Spread Compression Heatmap – Highlights compressed zones using yellow intensity, derived from historical spread analysis.
Composite Trend Scoring – Aggregates directional signals from each Cloud using your chosen weighting model.
Color-Coded Candles – Optional candle coloring reflects the real-time composite score.
UI Table – A toggleable info table shows slopes, compression levels, percentile ranks, and direction scores for each Cloud.
Gradient Cloud Styling – Apply gradient coloring from Cloud 1 to Cloud 4 for visual slope intensity.
Weight Aggregation Options – Use equal weighting, inverse-length weighting, or max pooling across Clouds to determine composite trend strength.
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🧪 How to Use the Indicator
1. Understand Trend Bias with Cloud Colors
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Each Cloud changes color based on its current slope:
Green indicates a rising trend.
Red indicates a falling trend.
Gray indicates a flat slope — often seen during chop or transitions.
Cloud 1 typically reflects short-term structure, while Cloud 4 represents long-term directional bias. Watch for multi-Cloud alignment — when all Clouds are green or red, the trend is strong. Divergence among Clouds often signals a potential shift.
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2. Use Compression Heat to Anticipate Breakouts
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The space between each Cloud’s top and bottom regression lines is measured, normalized, and analyzed over time. When this spread tightens relative to its history, the script highlights the band with a yellow compression glow .
This visual cue helps identify squeeze zones before volatility expands. If you see compression paired with a changing slope color (e.g., gray to green), this may indicate an impending breakout.
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3. Leverage the Optional Table UI
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The indicator includes a dynamic, floating table that displays real-time metrics per Cloud. These include:
Slope direction and value , with historical Min/Max reference.
Top and Bottom percentile ranks , showing how price sits within the Cloud range.
Current spread width , compared to its historical norms.
Composite score , which blends trend, slope, and compression for that Cloud.
You can customize the table’s position, theme, transparency, and whether to show a combined summary score in the header.
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4. Analyze Candle Color for Composite Signals
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When enabled, the indicator colors candles based on a weighted composite score. This score factors in:
The signed slope of each Cloud (up, down, or flat)
The percentile pressure from the top and bottom bands
The degree of spread compression
Expect green candles in bullish trend phases, red candles during bearish regimes, and gray candles in mixed or low-conviction zones.
Candle coloring provides a visual shorthand for market conditions , useful for intraday scanning or historical backtesting.
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🧰 Configuration Guidance
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To tailor the indicator to your strategy:
Use Cloud lengths like 21, 34, 55, and 89 for a balanced multi-timeframe view.
Adjust the slope threshold (default 0.05) to control how sensitive the trend coloring is.
Set the spread floor (e.g., 0.15) to tune when compression is detected and visualized.
Choose your weighting style : Inverse Length (favor faster bands), Equal, or Max Pooling (most aggressive).
Set composite weights to emphasize trend slope, percentile bias, or compression—depending on your market edge.
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✅ Best Practices
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Use aligned Cloud colors across all bands to confirm trend conviction.
Combine slope direction with compression glow for early breakout entry setups.
In choppy markets, watch for Clouds 1 and 2 turning flat while Clouds 3 and 4 remain directional — a sign of potential trend exhaustion or consolidation.
Keep the table enabled during backtesting to manually evaluate how each Cloud behaved during price turns and consolidations.
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📌 License & Usage Terms
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This script is provided under the Creative Commons Attribution-NonCommercial 4.0 International License .
✅ You are allowed to:
Use this script for personal or educational purposes
Study, learn, and adapt it for your own non-commercial strategies
❌ You are not allowed to:
Resell or redistribute the script without permission
Use it inside any paid product or service
Republish without giving clear attribution to the original author
For commercial licensing , private customization, or collaborations, please contact Joshua Danford directly.
BERLIN-MAX 1V.5BERLIN-MAX 1V.5 is a comprehensive trading indicator designed for TradingView that combines multiple advanced strategies and tools. It integrates EMA crossover signals, UT Bot logic with ATR-based trailing stops, customizable stop-loss and target multipliers per timeframe, Hull Moving Averages with color-coded trends, linear regression channels for support and resistance, and a multi-timeframe RSI and volume signal table. This script aims to provide clear entry and exit signals for scalping and swing trading, enhancing decision-making across different market conditions.
Adaptive Market Profile – Auto Detect & Dynamic Activity ZonesAdaptive Market Profile is an advanced indicator that automatically detects and displays the most relevant trend channel and market profile for any asset and timeframe. Unlike standard regression channel tools, this script uses a fully adaptive approach to identify the optimal period, providing you with the channel that best fits the current market dynamics. The calculation is based on maximizing the statistical significance of the trend using Pearson’s R coefficient, ensuring that the most relevant trend is always selected.
Within the selected channel, the indicator generates a dynamic market profile, breaking the price range into configurable zones and displaying the most active areas based on volume or the number of touches. This allows you to instantly identify high-activity price levels and potential support/resistance zones. The “most active lines” are plotted in real-time and always stay parallel to the channel, dynamically adapting to market structure.
Key features:
- Automatic detection of the optimal regression period: The script scans a wide range of lengths and selects the channel that statistically represents the strongest trend.
- Dynamic market profile: Visualizes the distribution of volume or price touches inside the trend channel, with customizable section count.
- Most active zones: Highlights the most traded or touched price levels as dynamic, parallel lines for precise support/resistance reading.
- Manual override: Optionally, users can select their own channel period for full control.
- Supports both linear and logarithmic charts: Simple toggle to match your chart scaling.
Use cases:
- Trend following and channel trading strategies.
- Quick identification of dynamic support/resistance and liquidity zones.
- Objective selection of the most statistically significant trend channel, without manual guesswork.
- Suitable for all assets and timeframes (crypto, stocks, forex, futures).
Originality:
This script goes beyond basic regression channels by integrating dynamic profile analysis and fully adaptive period detection, offering a comprehensive tool for modern technical analysts. The combination of trend detection, market profile, and activity zone mapping is unique and not available in TradingView built-ins.
Instructions:
Add Adaptive Market Profile to your chart. By default, the script automatically detects the optimal channel period and displays the corresponding regression channel with dynamic profile and activity zones. If you prefer manual control, disable “Auto trend channel period” and set your preferred period. Adjust profile settings as needed for your asset and timeframe.
For questions, suggestions, or further customization, contact Julien Eche (@Julien_Eche) directly on TradingView.
Dynamic S/R System - Pivot + ChannelDynamic S/R System - Pivot + Channel
A comprehensive Support & Resistance indicator combining dual methodologies for institutional-grade price level analysis
📊 CORE FEATURES
Dual Detection System
• Pivot-Based Levels - Historical turning points with intelligent touch counting
• Dynamic Channel S/R - Trend-aware linear regression boundaries
• Smart Level Management - Auto-merges similar levels, removes weak/outdated ones
Volume Integration
• Multi-timeframe volume analysis using EMA oscillator and spike detection
• Volume confirmation for all breakout signals to filter false moves
• Real-time volume status (Normal/High/Spike) in live information panel
Intelligent Touch Counting
• Automatic level validation through touch frequency analysis
• Strength classification with visual differentiation (colors/thickness)
• Level labels showing exact touch count (S3, R5, etc.)
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🎨 VISUAL ELEMENTS
Line System
Solid Lines: Pivot-based S/R levels
Dashed Lines: Dynamic channel boundaries
Color Coding:
• 🔵 Blue/🔴 Red: Standard support/resistance
• 🟠 Orange: Strong levels (multiple touches)
• 🟣 Purple: Channel S/R levels
Signal Labels
• "B" - Pivot S/R breakout with volume confirmation
• "CB" - Channel boundary breakout
• "Bull/Bear Wick" - False breakout detection (wick rejections)
Information Panel
Real-time analysis displays:
• Total resistance/support levels detected
• Closest S/R levels to current price
• Volume status and position relative to levels
• Current market position assessment
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✅ KEY ADVANTAGES
Multi-Method Validation
Combines historical pivot analysis with dynamic trend channels for comprehensive market view
False Breakout Protection
• Volume confirmation requirements
• Wick analysis to identify failed attempts
• Multiple validation criteria before signal generation
Adaptive Level Management
• Automatically updates as new pivots form
• Removes outdated/weak levels
• Maintains clean, relevant level display
Institutional-Grade Analysis
• Touch counting reveals institutional respect levels
• Volume integration shows smart money activity
• Strength classification identifies high-probability zones
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⏰ OPTIMAL USE CASES
Best Timeframes
• Daily - Primary recommendation for swing trading
• 4-Hour - Intraday analysis and entries
• Weekly - Long-term position planning
Ideal Markets
• Crypto pairs (especially ETH/BTC, BTC/USD)
• Forex majors with good volume data
• Large-cap stocks with institutional participation
Trading Applications
• Entry/exit planning around key S/R levels
• Breakout confirmation with volume validation
• Risk management using nearest S/R for stops
• Trend analysis through channel dynamics
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⚙️ CONFIGURATION GUIDELINES
Conservative Setup (Higher Confidence)
Min Pivot Strength: 3-4
Volume Threshold: 25-30%
Max Levels: 6-8
Aggressive Setup (More Signals)
Min Pivot Strength: 2
Volume Threshold: 15-20%
Max Levels: 10-12
🔔 ALERT SYSTEM
Breakout Alerts
• Resistance/Support breaks with volume confirmation
• Channel boundary violations
• Approaching strong S/R levels
Advanced Notifications
• Strong level approaches (within 0.5% of price)
• False breakout detection
• Volume spike confirmations
📈 TRADING STRATEGY GUIDE
Entry Strategy
1. Wait for price to approach identified S/R level
2. Confirm with volume analysis (spike/high volume preferred)
3. Watch for wick formations indicating rejection
4. Enter on confirmed breakout with volume or bounce with rejection
Risk Management
• Use nearest S/R level for stop placement
• Scale position size based on level strength (touch count)
• Monitor volume confirmation for exit signals
Market Context
• Combine with higher timeframe trend analysis
• Consider overall market sentiment and volatility
• Use channel direction for bias confirmation
Transform complex S/R analysis into actionable trading intelligence with institutional-level insights for professional trading decisions.
Bitcoin Power Law Clock [LuxAlgo]The Bitcoin Power Law Clock is a unique representation of Bitcoin prices proposed by famous Bitcoin analyst and modeler Giovanni Santostasi.
It displays a clock-like figure with the Bitcoin price and average lines as spirals, as well as the 12, 3, 6, and 9 hour marks as key points in the cycle.
🔶 USAGE
Giovanni Santostasi, Ph.D., is the creator and discoverer of the Bitcoin Power Law Theory. He is passionate about Bitcoin and has 12 years of experience analyzing it and creating price models.
As we can see in the above chart, the tool is super intuitive. It displays a clock-like figure with the current Bitcoin price at 10:20 on a 12-hour scale.
This tool only works on the 1D INDEX:BTCUSD chart. The ticker and timeframe must be exact to ensure proper functionality.
According to the Bitcoin Power Law Theory, the key cycle points are marked at the extremes of the clock: 12, 3, 6, and 9 hours. According to the theory, the current Bitcoin prices are in a frenzied bull market on their way to the top of the cycle.
🔹 Enable/Disable Elements
All of the elements on the clock can be disabled. If you disable them all, only an empty space will remain.
The different charts above show various combinations. Traders can customize the tool to their needs.
🔹 Auto scale
The clock has an auto-scale feature that is enabled by default. Traders can adjust the size of the clock by disabling this feature and setting the size in the settings panel.
The image above shows different configurations of this feature.
🔶 SETTINGS
🔹 Price
Price: Enable/disable price spiral, select color, and enable/disable curved mode
Average: Enable/disable average spiral, select color, and enable/disable curved mode
🔹 Style
Auto scale: Enable/disable automatic scaling or set manual fixed scaling for the spirals
Lines width: Width of each spiral line
Text Size: Select text size for date tags and price scales
Prices: Enable/disable price scales on the x-axis
Handle: Enable/disable clock handle
Halvings: Enable/disable Halvings
Hours: Enable/disable hours and key cycle points
🔹 Time & Price Dashboard
Show Time & Price: Enable/disable time & price dashboard
Location: Dashboard location
Size: Dashboard size
Bitcoin Power Law [LuxAlgo]The Bitcoin Power Law tool is a representation of Bitcoin prices first proposed by Giovanni Santostasi, Ph.D. It plots BTCUSD daily closes on a log10-log10 scale, and fits a linear regression channel to the data.
This channel helps traders visualise when the price is historically in a zone prone to tops or located within a discounted zone subject to future growth.
🔶 USAGE
Giovanni Santostasi, Ph.D. originated the Bitcoin Power-Law Theory; this implementation places it directly on a TradingView chart. The white line shows the daily closing price, while the cyan line is the best-fit regression.
A channel is constructed from the linear fit root mean squared error (RMSE), we can observe how price has repeatedly oscillated between each channel areas through every bull-bear cycle.
Excursions into the upper channel area can be followed by price surges and finishing on a top, whereas price touching the lower channel area coincides with a cycle low.
Users can change the channel areas multipliers, helping capture moves more precisely depending on the intended usage.
This tool only works on the daily BTCUSD chart. Ticker and timeframe must match exactly for the calculations to remain valid.
🔹 Linear Scale
Users can toggle on a linear scale for the time axis, in order to obtain a higher resolution of the price, (this will affect the linear regression channel fit, making it look poorer).
🔶 DETAILS
One of the advantages of the Power Law Theory proposed by Giovanni Santostasi is its ability to explain multiple behaviors of Bitcoin. We describe some key points below.
🔹 Power-Law Overview
A power law has the form y = A·xⁿ , and Bitcoin’s key variables follow this pattern across many orders of magnitude. Empirically, price rises roughly with t⁶, hash-rate with t¹² and the number of active addresses with t³.
When we plot these on log-log axes they appear as straight lines, revealing a scale-invariant system whose behaviour repeats proportionally as it grows.
🔹 Feedback-Loop Dynamics
Growth begins with new users, whose presence pushes the price higher via a Metcalfe-style square-law. A richer price pool funds more mining hardware; the Difficulty Adjustment immediately raises the hash-rate requirement, keeping profit margins razor-thin.
A higher hash rate secures the network, which in turn attracts the next wave of users. Because risk and Difficulty act as braking forces, user adoption advances as a power of three in time rather than an unchecked S-curve. This circular causality repeats without end, producing the familiar boom-and-bust cadence around the long-term power-law channel.
🔹 Scale Invariance & Predictions
Scale invariance means that enlarging the timeline in log-log space leaves the trajectory unchanged.
The same geometric proportions that described the first dollar of value can therefore extend to a projected million-dollar bitcoin, provided no catastrophic break occurs. Institutional ETF inflows supply fresh capital but do not bend the underlying slope; only a persistent deviation from the line would falsify the current model.
🔹 Implications
The theory assigns scarcity no direct role; iterative feedback and the Difficulty Adjustment are sufficient to govern Bitcoin’s expansion. Long-term valuation should focus on position within the power-law channel, while bubbles—sharp departures above trend that later revert—are expected punctuations of an otherwise steady climb.
Beyond about 2040, disruptive technological shifts could alter the parameters, but for the next order of magnitude the present slope remains the simplest, most robust guide.
Bitcoin behaves less like a traditional asset and more like a self-organising digital organism whose value, security, and adoption co-evolve according to immutable power-law rules.
🔶 SETTINGS
🔹 General
Start Calculation: Determine the start date used by the calculation, with any prior prices being ignored. (default - 15 Jul 2010)
Use Linear Scale for X-Axis: Convert the horizontal axis from log(time) to linear calendar time
🔹 Linear Regression
Show Regression Line: Enable/disable the central power-law trend line
Regression Line Color: Choose the colour of the regression line
Mult 1: Toggle line & fill, set multiplier (default +1), pick line colour and area fill colour
Mult 2: Toggle line & fill, set multiplier (default +0.5), pick line colour and area fill colour
Mult 3: Toggle line & fill, set multiplier (default -0.5), pick line colour and area fill colour
Mult 4: Toggle line & fill, set multiplier (default -1), pick line colour and area fill colour
🔹 Style
Price Line Color: Select the colour of the BTC price plot
Auto Color: Automatically choose the best contrast colour for the price line
Price Line Width: Set the thickness of the price line (1 – 5 px)
Show Halvings: Enable/disable dotted vertical lines at each Bitcoin halving
Halvings Color: Choose the colour of the halving lines
TrueTrend MaxRThe TrueTrend MaxR indicator is designed to identify the most consistent exponential price trend over extended periods. It uses statistical analysis on log-transformed prices to find the trendline that best fits historical price action, and highlights the most frequently tested or traded level within that trend channel.
For optimal results, especially on high timeframes such as weekly or monthly, it is recommended to use this indicator on charts set to logarithmic scale. This ensures proper visual alignment with the exponential nature of long-term price movements.
How it works
The indicator tests 50 different lookback periods, ranging from 300 to 1280 bars. For each period, it:
- Applies a linear regression on the natural logarithm of the price
- Computes the slope and intercept of the trendline
- Calculates the unbiased standard deviation from the regression line
- Measures the correlation strength using Pearson's R coefficient
The period with the highest Pearson R value is selected, meaning the trendline drawn corresponds to the log-scale trend with the best statistical fit.
Trendline and deviation bands
Once the optimal period is identified, the indicator plots:
- A main log-scale trendline
- Upper and lower bands, based on a user-defined multiple of the standard deviation
These bands help visualize how far price deviates from its core trend, and define the range of typical fluctuations.
Point of Control (POC)
Inside the trend channel, the space between upper and lower bands is divided into 15 logarithmic levels. The script evaluates how often price has interacted with each level, using one of two selectable methods:
- Touches: Counts the number of candles crossing each level
- Volume: Weighs each touch by the traded volume at that candle
The level with the highest cumulative interaction is considered the dynamic Point of Control (POC), and is plotted as a line.
Annualized performance and confidence display
When used on daily or weekly timeframes, the script also calculates the annualized return (CAGR) based on the detected trend, and displays:
- A performance estimate in percentage terms
- A textual label describing the confidence level based on the Pearson R value
Why this indicator is useful
- Automatically detects the most statistically consistent exponential trendline
- Designed for log-scale analysis, suited to long-term investment charts
- Highlights key price levels frequently visited or traded within the trend
- Provides objective, data-based trend and volatility insights
- Displays annualized growth rate and correlation strength for quick evaluation
Notes
- All calculations are performed only on the last bar
- No future data is used, and the script does not repaint
- Works on any instrument or timeframe, with optimal use on higher timeframes and logarithmic scaling
Linear Regression Slope The Linear Regression Slope provides a quantitative measure of trend direction. It fits a linear regression line to the past N closing prices and calculates the slope, representing the average rate of price change per bar.
To ensure comparability across assets and timeframes, the slope is normalized by the ATR over a shorter window. This produces a volatility-adjusted measure which allows for the slope to be interpreted relative to typical price fluctuations.
Mathematically, the slope is derived by minimizing the sum of squared deviations between actual prices and the fitted regression line. A positive normalized slope indicate upwards movement; a negative slope indicate downwards movement. Persistent values near zero could indicate an absence of clear trend, with price dominated by short-term fluctuations or noise.
The definition of a trend depends on the period of observation. The lookback setting should be set based on to the desired timeframe. Shorter lookbacks will respond faster to recent changes but may be more sensitive to noise, while longer lookbacks will emphasize broader structures.
While effective at quantifying existing trends, this method is not predictive. Sudden regime changes, volatility shocks, and non-linear dynamics can all cause rapid slope reversals. Therefore, it is best applied as part of a broader analytical framework.
In summary, the Linear Regression Slope quantifies price direction and serves as a measurable supplement to the visual assessment of trends on price charts.
Additional Features:
Option to display or hide the normalized slope line.
Option to enable background coloring when the slope is above or below zero.
LinReg Heikin Ashi CandlesLinear Regression Heikin Ashi Candles will dramatically change how the candlesticks on your chart will appear. This script creates Heikin Ashi candles from the existing candlesticks and then applies wickless Linear Regression candles as an overlay. The result is an ultra smoothed 'Renko-like' chart that remains time-based and responsive.
Key Features:
Heikin Ashi Base: Provides a smoother representation of price trends by filtering out noise.
Linear Regression Candles on Heikin Ashi: Plots Linear Regression lines as candles on the Heikin Ashi chart, potentially highlighting the immediate trend direction and momentum within the smoothed data. Wicks are intentionally removed for a clearer focus on the linear progression.
Tillson T3 Moving Averages: Includes fast and slow T3 Moving Averages with customizable length and alpha. These smoothed moving averages can help identify trend direction and potential crossover signals. Users can toggle their visibility.
Volatility Bands: Integrates Volatility Bands based on Average True Range (ATR) with customizable length, ATR type (RMA, SMA, EMA, WMA), and inner/outer multipliers. These bands help gauge price volatility and potential reversal zones. Users can toggle the visibility of the basis line.
Customizable Colors: Allows users to customize the colors of the Linear Regression Heikin Ashi bullish and bearish candles.
How to Use:
This is an overlay on your chart so you'll need to 'hide' the existing candlesticks on your chart.
This indicator can be used on any timeframe from seconds to days to quickly identify market trend, gauge volatility, and potentially find entry/exit points. Consider looking for confluence between the candle color/direction, T3 MA crossovers, and price interaction with the Volatility Bands.
Note: This indicator plots Linear Regression directly on Heikin Ashi candles, removing wicks for a focus on the linear trend within the smoothed data. Adjust the input parameters to suit your trading style and the specific market conditions.
HUGE CREDIT to ugurvu who originally created the Linear Regression Candles indicator that my indicator pulls code from.
Change of Character FanChange of Character Fan
Overview
The Change of Character Fan is designed to help traders detect shifts (changes of character) in market direction and sentiment before they become fully visible through traditional candlestick analysis. Instead of relying solely on the shape or close of candlesticks, this indicator offers a direct, real-time look at the internal price action occurring within a single bar. This visibility into intrabar dynamics can potentially allow traders to enter or exit trades earlier, minimize false signals, and reduce their dependence on multiple lower-timeframe charts.
How it Works:
The indicator plots a "fan" consisting of five distinct slope lines within the current bar. Each line represents the internal trend of price movement based on user-defined lower timeframe data intervals.
By default, these intervals are set to 3, 5, 8, 13, and 21 samples from 1-second timeframe data.
Each line only appears when it has collected the minimum required number of intrabar data points.
The fan lines use a progressive opacity scale (lighter to darker), visually highlighting the confidence level or probability of directional continuation within the current bar.
At the open of every new bar, the fan disappears completely and gradually reappears as new data is gathered, ensuring clarity and eliminating outdated signals.
Understanding the Mathematics: Linear Regression Model
This indicator is built around the concept of a linear regression model. Linear regression is a statistical technique used to model and analyze relationships between variables—in this case, time (independent variable) and price (dependent variable).
How Linear Regression Works:
Linear regression fits a straight line (called a "line of best fit") through a set of data points, minimizing the overall distance between each point and the line itself.
Mathematically, this is achieved by minimizing the squared differences (errors) between the observed values (actual prices) and the predicted values (prices on the line).
The linear model used here can be expressed in the form:
y = mx + b
where:
𝑦
y is the predicted price,
𝑥
x represents time (each data sample interval),
𝑚
m is the slope of the line, representing the direction and velocity of the trend,
𝑏
b is the intercept (the theoretical price when x=0).
Why a Linear Model is Beneficial in this Indicator:
Simplicity and Reliability: Linear regression is simple, robust, and widely accepted as a baseline predictive model. It requires minimal computational resources, providing instant updates in real-time trading conditions.
Immediate Directional Feedback: The slope derived from linear regression immediately communicates the directional tendency of recent price action. A positive slope indicates upward pressure, and a negative slope signals downward pressure.
Noise Reduction: Even when price fluctuations are noisy or erratic, linear regression summarizes overall direction clearly, making it easier to detect genuine directional shifts (change of character) rather than random price noise.
Intrabar Analysis: Traditional candlestick analysis relies on fully formed candles, potentially delaying signals. By using linear regression on very short-term (intrabar) data, traders can detect shifts in momentum more quickly, providing an earlier signal than conventional candle patterns alone.
Practical Application:
This indicator helps traders to visually identify:
Early Trend Reversals: Intrabar analysis reveals momentum shifts potentially signaling reversals before they become obvious on conventional candles.
Momentum Continuations: Confidence is gained when all lines in the fan are clearly pointing in the same direction, indicating strong intrabar conviction.
Reduced False Signals: Traditional candlestick signals (e.g., hammer candles) sometimes produce false signals due to intrabar noise. By looking directly into intrabar dynamics, traders gain better context on whether candle patterns reflect genuine directional change or merely noise.
Important Requirements and Recommendations:
Subscription Requirements:
A TradingView subscription that supports sub-minute data (e.g., 1-second or 5-second resolution) is strongly recommended.
If your subscription doesn't include this data granularity, you must use a 1-minute lower timeframe, significantly reducing responsiveness. In this scenario, it's best suited for a 15-minute or higher chart, adjusting intervals to shorter periods.
Live Data Essential:
Real-time market data subscription is essential for the accuracy and effectiveness of this indicator.
Using delayed data reduces responsiveness and weakens the indicator's primary advantage.
Recommended Settings for Different Chart Timeframes:
1-minute chart: Use 1-second lower timeframe intervals (default intervals: 3, 5, 8, 13, 21).
5-minute chart: Adjust to a 5- or 10-second lower timeframe, possibly reducing intervals to shorter periods (e.g., 3, 5, 8, 10, 12).
15-minute or higher charts: Adjust lower timeframe to 1-minute if granular data is unavailable, with reduced interval lengths to maintain responsiveness.
Conclusion:
The Change of Character Fan empowers traders with early insight into directional shifts within each candle, significantly enhancing reaction speed, signal accuracy, and reducing dependency on multiple charts. Built on robust linear regression mathematics, it combines clarity, responsiveness, and ease-of-use in a powerful intrabar analysis tool.
Trade smarter, see sooner, and react faster.
Rolling Beta against SPY📈 Pine Script Showcase: Rolling Beta Against SPY
Understanding how your favorite stock or ETF moves in relation to a benchmark like the S&P 500 can offer powerful insights into risk and exposure. This script calculates and visualizes the rolling beta of any asset versus the SPY ETF (which tracks the S&P 500).
🧠 What Is Beta?
Beta measures the sensitivity of an asset's returns to movements in the broader market. A beta of:
- 1.0 means the asset moves in lockstep with SPY,
- >1.0 indicates higher volatility than the market,
- <1.0 implies lower volatility or possible defensive behavior,
- <0 suggests inverse correlation (e.g., hedging instruments).
🧮 How It Works
This script computes rolling beta over a user-defined window (default = 60 periods) using classic linear regression math:
- Calculates daily returns for both the asset and SPY.
- Computes covariance between the two return streams.
- Divides by the variance of SPY returns to get beta.
⚙️ Customization
You can adjust the window size to control the smoothing:
- Shorter windows capture recent volatility changes,
- Longer windows give more stable, long-term estimates.
📊 Visual Output
The script plots the beta series dynamically, allowing you to observe how your asset’s correlation to SPY evolves over time. This is especially useful in regime-change environments or during major macroeconomic shifts.
💡 Use Cases
- Portfolio construction: Understand how your assets co-move with the market.
- Risk management: Detect when beta spikes—potentially signaling higher market sensitivity.
- Market timing: Use beta shifts to infer changing investor sentiment or market structure.
📌 Pro Tip: Combine this rolling beta with volatility, Sharpe ratio, or correlation tracking for a more robust factor-based analysis.
Ready to add a layer of quantitative insight to your chart? Add the script to your watchlist and start analyzing your favorite tickers against SPY today!
Leavitt Convolution ProbabilityTechnical Analysis of Markets with Leavitt Market Projections and Associated Convolution Probability
The aim of this study is to present an innovative approach to market analysis based on the research "Leavitt Market Projections." This technical tool combines one indicator and a probability function to enhance the accuracy and speed of market forecasts.
Key Features
Advanced Indicators : the script includes the Convolution line and a probability oscillator, designed to anticipate market changes. These indicators provide timely signals and offer a clear view of price dynamics.
Convolution Probability Function : The Convolution Probability (CP) is a key element of the script. A significant increase in this probability often precedes a market decline, while a decrease in probability can signal a bullish move. The Convolution Probability Function:
At each bar, i, the linear regression routine finds the two parameters for the straight line: y=mix+bi.
Standard deviations can be calculated from the sequence of slopes, {mi}, and intercepts, {bi}.
Each standard deviation has a corresponding probability.
Their adjusted product is the Convolution Probability, CP. The construction of the Convolution Probability is straightforward. The adjusted product is the probability of one times 1− the probability of the other.
Customizable Settings : Users can define oversold and overbought levels, as well as set an offset for the linear regression calculation. These options allow for tailoring the script to individual trading strategies and market conditions.
Statistical Analysis : Each analyzed bar generates regression parameters that allow for the calculation of standard deviations and associated probabilities, providing an in-depth view of market dynamics.
The results from applying this technical tool show increased accuracy and speed in market forecasts. The combination of Convolution indicator and the probability function enables the identification of turning points and the anticipation of market changes.
Additional information:
Leavitt, in his study, considers the SPY chart.
When the Convolution Probability (CP) is high, it indicates that the probability P1 (related to the slope) is high, and conversely, when CP is low, P1 is low and P2 is high.
For the calculation of probability, an approximate formula of the Cumulative Distribution Function (CDF) has been used, which is given by: CDF(x)=21(1+erf(σ2x−μ)) where μ is the mean and σ is the standard deviation.
For the calculation of probability, the formula used in this script is: 0.5 * (1 + (math.sign(zSlope) * math.sqrt(1 - math.exp(-0.5 * zSlope * zSlope))))
Conclusions
This study presents the approach to market analysis based on the research "Leavitt Market Projections." The script combines Convolution indicator and a Probability function to provide more precise trading signals. The results demonstrate greater accuracy and speed in market forecasts, making this technical tool a valuable asset for market participants.
Linear Regression Volume Profile [ChartPrime]LR VolumeProfile
This indicator combines a Linear Regression channel with a dynamic volume profile, giving traders a powerful way to visualize both directional price movement and volume concentration along the trend.
⯁ KEY FEATURES
Linear Regression Channel: Draws a statistically fitted channel to track the market trend over a defined period.
Volume Profile Overlay: Splits the channel into multiple horizontal levels and calculates volume traded within each level.
Percentage-Based Labels: Displays each level's share of total volume as a percentage, offering a clean way to see high and low volume zones.
Gradient Bars: Profile bars are colored using a gradient scale from yellow (low volume) to red (high volume), making it easy to identify key interest areas.
Adjustable Profile Width and Resolution: Users can change the width of profile bars and spacing between levels.
Channel Direction Indicator: An arrow inside a floating label shows the direction (up or down) of the current linear regression slope.
Level Style Customization: Choose from solid, dashed, or dotted lines for visual preference.
⯁ HOW TO USE
Use the Linear Regression channel to determine the dominant price trend direction.
Analyze the volume bars to spot key levels where the majority of volume was traded—these act as potential support/resistance zones.
Pay attention to the largest profile bars—these often mark zones of institutional interest or price consolidation.
The arrow label helps quickly assess whether the trend is upward or downward.
Combine this tool with price action or momentum indicators to build high-confidence trading setups.
⯁ CONCLUSION
LR Volume Profile is a precision tool for traders who want to merge trend analysis with volume insight. By integrating linear regression trendlines with a clean and readable volume distribution, this indicator helps traders find price levels that matter the most—backed by volume, trend, and structure. Whether you're spotting high-volume nodes or gauging directional flow, this toolkit elevates your decision-making process with clarity and depth.
Multi-Anchored Linear Regression Channels [TANHEF]█ Overview:
The 'Multi-Anchored Linear Regression Channels ' plots multiple dynamic regression channels (or bands) with unique selectable calculation types for both regression and deviation. It leverages a variety of techniques, customizable anchor sources to determine regression lengths, and user-defined criteria to highlight potential opportunities.
Before getting started, it's worth exploring all sections, but make sure to review the Setup & Configuration section in particular. It covers key parameters like anchor type, regression length, bias, and signal criteria—essential for aligning the tool with your trading strategy.
█ Key Features:
⯁ Multi-Regression Capability:
Plot up to three distinct regression channels and/or bands simultaneously, each with customizable anchor types to define their length.
⯁ Regression & Deviation Methods:
Regressions Types:
Standard: Uses ordinary least squares to compute a simple linear trend by averaging the data and deriving a slope and endpoints over the lookback period.
Ridge: Introduces L2 regularization to stabilize the slope by penalizing large coefficients, which helps mitigate multicollinearity in the data.
Lasso: Uses L1 regularization through soft-thresholding to shrink less important coefficients, yielding a simpler model that highlights key trends.
Elastic Net: Combines L1 and L2 penalties to balance coefficient shrinkage and selection, producing a robust weighted slope that handles redundant predictors.
Huber: Implements the Huber loss with iteratively reweighted least squares (IRLS) and EMA-style weights to reduce the impact of outliers while estimating the slope.
Least Absolute Deviations (LAD): Reduces absolute errors using iteratively reweighted least squares (IRLS), yielding a slope less sensitive to outliers than squared-error methods.
Bayesian Linear: Merges prior beliefs with weighted data through Bayesian updating, balancing the prior slope with data evidence to derive a probabilistic trend.
Deviation Types:
Regressive Linear (Reverse): In reverse order (recent to oldest), compute weighted squared differences between the data and a line defined by a starting value and slope.
Progressive Linear (Forward): In forward order (oldest to recent), compute weighted squared differences between the data and a line defined by a starting value and slope.
Balanced Linear: In forward order (oldest to newest), compute regression, then pair to source data in reverse order (newest to oldest) to compute weighted squared differences.
Mean Absolute: Compute weighted absolute differences between each data point and its regression line value, then aggregate them to yield an average deviation.
Median Absolute: Determine the weighted median of the absolute differences between each data point and its regression line value to capture the central tendency of deviations.
Percent: Compute deviation as a percentage of a base value by multiplying that base by the specified percentage, yielding symmetric positive and negative deviations.
Fitted: Compare a regression line with high and low series values by computing weighted differences to determine the maximum upward and downward deviations.
Average True Range: Iteratively compute the weighted average of absolute differences between the data and its regression line to yield an ATR-style deviation measure.
Bias:
Bias: Applies EMA or inverse-EMA style weighting to both Regression and/or Deviation, emphasizing either recent or older data.
⯁ Customizable Regression Length via Anchors:
Anchor Types:
Fixed: Length.
Bar-Based: Bar Highest/Lowest, Volume Highest/Lowest, Spread Highest/Lowest.
Correlation: R Zero, R Highest, R Lowest, R Absolute.
Slope: Slope Zero, Slope Highest, Slope Lowest, Slope Absolute.
Indicator-Based: Indicators Highest/Lowest (ADX, ATR, BBW, CCI, MACD, RSI, Stoch).
Time-Based: Time (Day, Week, Month, Quarter, Year, Decade, Custom).
Session-Based: Session (Tokyo, London, New York, Sydney, Custom).
Event-Based: Earnings, Dividends, Splits.
External: Input Source Highest/Lowest.
Length Selection:
Maximum: The highest allowed regression length (also fixed value of “Length” anchor).
Minimum: The shortest allowed length, ensuring enough bars for a valid regression.
Step: The sampling interval (e.g., 1 checks every bar, 2 checks every other bar, etc.). Increasing the step reduces the loading time, most applicable to “Slope” and “R” anchors.
Adaptive lookback:
Adaptive Lookback: Enable to display regression regardless of too few historical bars.
⯁ Selecting Bias:
Bias applies separately to regression and deviation.
Positive values emphasize recent data (EMA-style), negative invert, and near-zero maintains balance. (e.g., a length 100, bias +1 gives the newest price ~7× more weight than the oldest).
It's best to apply bias to both (regression and deviation) or just the deviation. Biasing only regression may distort deviation visually, while biasing both keeps their relationship intuitive. Using bias only for deviation scales it without altering regression, offering unique analysis.
⯁ Scale Awareness:
Supports linear and logarithmic price scaling, the regression and deviations adjust accordingly.
⯁ Signal Generation & Alerts:
Customizable entry/exit signals and alerts, detailed in the dedicated section below.
⯁ Visual Enhancements & Real-World Examples:
Optional on-chart table display summarizing regression input criteria (display type, anchor type, source, regression type, regression bias, deviation type, deviation bias, deviation multiplier) and key calculated metrics (regression length, slope, Pearson’s R, percentage position within deviations, etc.) for quick reference.
█ Understanding R (Pearson Correlation Coefficient):
Pearson’s R gauges data alignment to a straight-line trend within the regression length:
Range: R varies between –1 and +1.
R = +1 → Perfect positive correlation (strong uptrend).
R = 0 → No linear relationship detected.
R = –1 → Perfect negative correlation (strong downtrend).
This script uses Pearson’s R as an anchor, adjusting regression length to target specific R traits. Strong R (±1) follows the regression channel, while weak R (0) shows inconsistency.
█ Understanding the Slope:
The slope is the direction and rate at which the regression line rises or falls per bar:
Positive Slope (>0): Uptrend – Steeper means faster increase.
Negative Slope (<0): Downtrend – Steeper means sharper drop.
Zero or Near-Zero Slope: Sideways – Indicating range-bound conditions.
This script uses highest and lowest slope as an anchor, where extremes highlight strong moves and trend lines, while values near zero indicate sideways action and possible support/resistance.
█ Setup & Configuration:
Whether you’re new to this script or want to quickly adjust all critical parameters, the panel below shows the main settings available. You can customize everything from the anchor type and maximum length to the bias, signal conditions, and more.
Scale (select Log Scale for logarithmic, otherwise linear scale).
Display (regression channel and/or bands).
Anchor (how regression length is determined).
Length (control bars analyzed):
• Max – Upper limit.
• Min – Prevents regression from becoming too short.
• Step – Controls scanning precision; increasing Step reduces load time.
Regression:
• Type – Calculation method.
• Bias – EMA-style emphasis (>0=new bars weighted more; <0=old bars weighted more).
Deviation:
• Type – Calculation method.
• Bias – EMA-style emphasis (>0=new bars weighted more; <0=old bars weighted more).
• Multiplier - Adjusts Upper and Lower Deviation.
Signal Criteria:
• % (Price vs Deviation) – (0% = lower deviation, 50% = regression, 100% = upper deviation).
• R – (0 = no correlation, ±1 = perfect correlation; >0 = +slope, <0 = -slope).
Table (analyze table of input settings, calculated results, and signal criteria).
Adaptive Lookback (display regression while too few historical bars).
Multiple Regressions (steps 2 to 7 apply to #1, #2, and #3 regressions).
█ Signal Generation & Alerts:
The script offers customizable entry and exit signals with flexible criteria and visual cues (background color, dots, or triangles). Alerts can also be triggered for these opportunities.
Percent Direction Criteria:
(0% = lower deviation, 50% = regression line, 100% = upper deviation)
Above %: Triggers if price is above a specified percent of the deviation channel.
Below %: Triggers if price is below a specified percent of the deviation channel.
(Blank): Ignores the percent‐based condition.
Pearson's R (Correlation) Direction Criteria:
(0 = no correlation, ±1 = perfect correlation; >0 = positive slope, <0 = negative slope)
Above R / Below R: Compares the correlation to a threshold.
Above│R│ / Below│R│: Uses absolute correlation to focus on strength, ignoring direction.
Zero to R: Checks if R is in the 0-to-threshold range.
(Blank): Ignores correlation-based conditions.
█ User Tips & Best Practices:
Choose an anchor type that suits your strategy, “Bar Highest/Lowest” automatically spots commonly used regression zones, while “│R│ Highest” targets strong linear trends.
Consider enabling or disabling the Adaptive Lookback feature to ensure you always have a plotted regression if your chart doesn’t meet the maximum-length requirement.
Use a small Step size (1) unless relying on R-correlation or slope-based anchors as the are time-consuming to calculate. Larger steps speed up calculations but reduce precision.
Fine-tune settings such as lookback periods, regression bias, and deviation multipliers, or trend strength. Small adjustments can significantly affect how channels and signals behave.
To reduce loading time , show only channels (not bands) and disable signals, this limits calculations to the last bar and supports more extreme criteria.
Use the table display to monitor anchor type, calculated length, slope, R value, and percent location at a glance—especially if you have multiple regressions visible simultaneously.
█ Conclusion:
With its blend of advanced regression techniques, flexible deviation options, and a wide range of anchor types, this indicator offers a highly adaptable linear regression channeling system. Whether you're anchoring to time, price extremes, correlation, slope, or external events, the tool can be shaped to fit a variety of strategies. Combined with customizable signals and alerts, it may help highlight areas of confluence and support a more structured approach to identifying potential opportunities.
LinearRegressionLibrary "LinearRegression"
Calculates a variety of linear regression and deviation types, with optional emphasis weighting. Additionally, multiple of slope and Pearson’s R calculations.
calcSlope(_src, _len, _condition)
Calculates the slope of a linear regression over the specified length.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The length of the lookback period for the linear regression.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast for efficiency.
Returns: (float) The slope of the linear regression.
calcReg(_src, _len, _condition)
Calculates a basic linear regression, returning y1, y2, slope, and average.
Parameters:
_src (float) : (float) The source data series.
_len (int) : (int) The length of the lookback period.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: (float ) An array of 4 values: .
calcRegStandard(_src, _len, _emphasis, _condition)
Calculates an Standard linear regression with optional emphasis.
Parameters:
_src (float) : (series float) The source data series.
_len (int) : (int) The length of the lookback period.
_emphasis (float) : (float) The emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: (float ) .
calcRegRidge(_src, _len, lambda, _emphasis, _condition)
Calculates a ridge regression with optional emphasis.
Parameters:
_src (float) : (float) The source data series.
_len (int) : (int) The length of the lookback period.
lambda (float) : (float) The ridge regularization parameter.
_emphasis (float) : (float) The emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: (float ) .
calcRegLasso(_src, _len, lambda, _emphasis, _condition)
Calculates a Lasso regression with optional emphasis.
Parameters:
_src (float) : (float) The source data series.
_len (int) : (int) The length of the lookback period.
lambda (float) : (float) The Lasso regularization parameter.
_emphasis (float) : (float) The emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: (float ) .
calcElasticNetLinReg(_src, _len, lambda1, lambda2, _emphasis, _condition)
Calculates an Elastic Net regression with optional emphasis.
Parameters:
_src (float) : (float) The source data series.
_len (int) : (int) The length of the lookback period.
lambda1 (float) : (float) L1 regularization parameter (Lasso).
lambda2 (float) : (float) L2 regularization parameter (Ridge).
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: (float ) .
calcRegHuber(_src, _len, delta, iterations, _emphasis, _condition)
Calculates a Huber regression using Iteratively Reweighted Least Squares (IRLS).
Parameters:
_src (float) : (float) The source data series.
_len (int) : (int) The length of the lookback period.
delta (float) : (float) Huber threshold parameter.
iterations (int) : (int) Number of IRLS iterations.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: (float ) .
calcRegLAD(_src, _len, iterations, _emphasis, _condition)
Calculates a Least Absolute Deviations (LAD) regression via IRLS.
Parameters:
_src (float) : (float) The source data series.
_len (int) : (int) The length of the lookback period.
iterations (int) : (int) Number of IRLS iterations for LAD.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: (float ) .
calcRegBayesian(_src, _len, priorMean, priorSpan, sigma, _emphasis, _condition)
Calculates a Bayesian linear regression with optional emphasis.
Parameters:
_src (float) : (float) The source data series.
_len (int) : (int) The length of the lookback period.
priorMean (float) : (float) The prior mean for the slope.
priorSpan (float) : (float) The prior variance (or span) for the slope.
sigma (float) : (float) The assumed standard deviation of residuals.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: (float ) .
calcRFromLinReg(_src, _len, _slope, _average, _y1, _condition)
Calculates the Pearson correlation coefficient (R) based on linear regression parameters.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The length of the lookback period.
_slope (float) : (float) The slope of the linear regression.
_average (float) : (float) The average value of the source data series.
_y1 (float) : (float) The starting point (y-intercept of the oldest bar) for the linear regression.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast for efficiency.
Returns: (float) The Pearson correlation coefficient (R) adjusted for the direction of the slope.
calcRFromSource(_src, _len, _condition)
Calculates the correlation coefficient (R) using a specified length and source data.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The length of the lookback period.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast for efficiency.
Returns: (float) The correlation coefficient (R).
calcSlopeLengthZero(_src, _len, _minLen, _step, _condition)
Identifies the length at which the slope is flattest (closest to zero).
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The maximum lookback length to consider (minimum of 2).
_minLen (int) : (int) The minimum length to start from (cannot exceed the max length).
_step (int) : (int) The increment step for lengths.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.
Returns: (int) The length at which the slope is flattest.
calcSlopeLengthHighest(_src, _len, _minLen, _step, _condition)
Identifies the length at which the slope is highest.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The maximum lookback length (minimum of 2).
_minLen (int) : (int) The minimum length to start from.
_step (int) : (int) The step for incrementing lengths.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.
Returns: (int) The length at which the slope is highest.
calcSlopeLengthLowest(_src, _len, _minLen, _step, _condition)
Identifies the length at which the slope is lowest.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The maximum lookback length (minimum of 2).
_minLen (int) : (int) The minimum length to start from.
_step (int) : (int) The step for incrementing lengths.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.
Returns: (int) The length at which the slope is lowest.
calcSlopeLengthAbsolute(_src, _len, _minLen, _step, _condition)
Identifies the length at which the absolute slope value is highest.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The maximum lookback length (minimum of 2).
_minLen (int) : (int) The minimum length to start from.
_step (int) : (int) The step for incrementing lengths.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.
Returns: (int) The length at which the absolute slope value is highest.
calcRLengthZero(_src, _len, _minLen, _step, _condition)
Identifies the length with the lowest absolute R value.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The maximum lookback length (minimum of 2).
_minLen (int) : (int) The minimum length to start from.
_step (int) : (int) The step for incrementing lengths.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.
Returns: (int) The length with the lowest absolute R value.
calcRLengthHighest(_src, _len, _minLen, _step, _condition)
Identifies the length with the highest R value.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The maximum lookback length (minimum of 2).
_minLen (int) : (int) The minimum length to start from.
_step (int) : (int) The step for incrementing lengths.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.
Returns: (int) The length with the highest R value.
calcRLengthLowest(_src, _len, _minLen, _step, _condition)
Identifies the length with the lowest R value.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The maximum lookback length (minimum of 2).
_minLen (int) : (int) The minimum length to start from.
_step (int) : (int) The step for incrementing lengths.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.
Returns: (int) The length with the lowest R value.
calcRLengthAbsolute(_src, _len, _minLen, _step, _condition)
Identifies the length with the highest absolute R value.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The maximum lookback length (minimum of 2).
_minLen (int) : (int) The minimum length to start from.
_step (int) : (int) The step for incrementing lengths.
_condition (bool) : (bool) Flag to enable calculation. Set to true to calculate on every bar; otherwise, set to barstate.islast.
Returns: (int) The length with the highest absolute R value.
calcDevReverse(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)
Calculates the regressive linear deviation in reverse order, with optional emphasis on recent data.
Parameters:
_src (float) : (float) The source data.
_len (int) : (int) The length of the lookback period.
_slope (float) : (float) The slope of the linear regression.
_y1 (float) : (float) The y-intercept (oldest bar) of the linear regression.
_inputDev (float) : (float) The input deviation multiplier.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: A 2-element tuple: .
calcDevForward(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)
Calculates the progressive linear deviation in forward order (oldest to most recent bar), with optional emphasis.
Parameters:
_src (float) : (float) The source data array, where _src is oldest and _src is most recent.
_len (int) : (int) The length of the lookback period.
_slope (float) : (float) The slope of the linear regression.
_y1 (float) : (float) The y-intercept of the linear regression (value at the most recent bar, adjusted by slope).
_inputDev (float) : (float) The input deviation multiplier.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: A 2-element tuple: .
calcDevBalanced(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)
Calculates the balanced linear deviation with optional emphasis on recent or older data.
Parameters:
_src (float) : (float) Source data array, where _src is the most recent and _src is the oldest.
_len (int) : (int) The length of the lookback period.
_slope (float) : (float) The slope of the linear regression.
_y1 (float) : (float) The y-intercept of the linear regression (value at the oldest bar).
_inputDev (float) : (float) The input deviation multiplier.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: A 2-element tuple: .
calcDevMean(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)
Calculates the mean absolute deviation from a forward-applied linear trend (oldest to most recent), with optional emphasis.
Parameters:
_src (float) : (float) The source data array, where _src is the most recent and _src is the oldest.
_len (int) : (int) The length of the lookback period.
_slope (float) : (float) The slope of the linear regression.
_y1 (float) : (float) The y-intercept (oldest bar) of the linear regression.
_inputDev (float) : (float) The input deviation multiplier.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: A 2-element tuple: .
calcDevMedian(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)
Calculates the median absolute deviation with optional emphasis on recent data.
Parameters:
_src (float) : (float) The source data array (index 0 = oldest, index _len - 1 = most recent).
_len (int) : (int) The length of the lookback period.
_slope (float) : (float) The slope of the linear regression.
_y1 (float) : (float) The y-intercept (oldest bar) of the linear regression.
_inputDev (float) : (float) The deviation multiplier.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns:
calcDevPercent(_y1, _inputDev, _condition)
Calculates the percent deviation from a given value and a specified percentage.
Parameters:
_y1 (float) : (float) The base value from which to calculate deviation.
_inputDev (float) : (float) The deviation percentage.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: A 2-element tuple: .
calcDevFitted(_len, _slope, _y1, _emphasis, _condition)
Calculates the weighted fitted deviation based on high and low series data, showing max deviation, with optional emphasis.
Parameters:
_len (int) : (int) The length of the lookback period.
_slope (float) : (float) The slope of the linear regression.
_y1 (float) : (float) The Y-intercept (oldest bar) of the linear regression.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: A 2-element tuple: .
calcDevATR(_src, _len, _slope, _y1, _inputDev, _emphasis, _condition)
Calculates an ATR-style deviation with optional emphasis on recent data.
Parameters:
_src (float) : (float) The source data (typically close).
_len (int) : (int) The length of the lookback period.
_slope (float) : (float) The slope of the linear regression.
_y1 (float) : (float) The Y-intercept (oldest bar) of the linear regression.
_inputDev (float) : (float) The input deviation multiplier.
_emphasis (float) : (float) Emphasis factor: 0 for equal weight; >0 emphasizes recent bars; <0 emphasizes older bars.
_condition (bool) : (bool) Flag to enable calculation (true = calculate).
Returns: A 2-element tuple: .
calcPricePositionPercent(_top, _bot, _src)
Calculates the percent position of a price within a linear regression channel. Top=100%, Bottom=0%.
Parameters:
_top (float) : (float) The top (positive) deviation, corresponding to 100%.
_bot (float) : (float) The bottom (negative) deviation, corresponding to 0%.
_src (float) : (float) The source price.
Returns: (float) The percent position within the channel.
plotLinReg(_len, _y1, _y2, _slope, _devTop, _devBot, _scaleTypeLog, _lineWidth, _extendLines, _channelStyle, _colorFill, _colUpLine, _colDnLine, _colUpFill, _colDnFill)
Plots the linear regression line and its deviations, with configurable styles and fill.
Parameters:
_len (int) : (int) The lookback period for the linear regression.
_y1 (float) : (float) The starting y-value of the regression line.
_y2 (float) : (float) The ending y-value of the regression line.
_slope (float) : (float) The slope of the regression line (used to determine line color).
_devTop (float) : (float) The top deviation to add to the line.
_devBot (float) : (float) The bottom deviation to subtract from the line.
_scaleTypeLog (bool) : (bool) Use a log scale if true; otherwise, linear scale.
_lineWidth (int) : (int) The width of the plotted lines.
_extendLines (string) : (string) How lines should extend (none, left, right, both).
_channelStyle (string) : (string) The style of the channel lines (solid, dashed, dotted).
_colorFill (bool) : (bool) Whether to fill the space between the top and bottom deviation lines.
_colUpLine (color) : (color) Line color when slope is positive.
_colDnLine (color) : (color) Line color when slope is negative.
_colUpFill (color) : (color) Fill color when slope is positive.
_colDnFill (color) : (color) Fill color when slope is negative.
Autocorrelation Price Forecasting [The Quant Science]Discover how to predict future price movements using autocorrelation and linear regression models to identify potential trading opportunities.
An advanced model to predict future price movements using autocorrelation and linear regression. This script helps identify recurring market cycles and calculates potential gains, with clear visual signals for quick and informed decisions.
Main function
This script leverages an autocorrelation model to estimate the future price of an asset based on historical price relationships. It also integrates linear regression on percentage returns to provide more accurate predictions of price movements.
Insights types
1) Red label on a green candle: Bearish forecast and swing trading opportunity.
2) Red label on a red candle: Bearish forecast and trend-following opportunity.
3) Green label on a red candle: Bullish forecast and swing trading opportunity.
4) Green label on a green candle: Bullish forecast and trend-following opportunity.
IMPORTANT!
The indicator displays a future price forecast. When negative, it estimates a future price drop.
When positive, it estimates a future price increase.
Key Features
Customizable inputs
Analysis Length: number of historical bars used for autocorrelation calculation. Adjustable between 1 and 200.
Forecast Colors: customize colors for bullish and bearish signals.
Visual insights
Labels: hypothetical gains or losses are displayed as labels above or below the bars.
Dynamic coloring: bullish (green) and bearish (red) signals are highlighted directly on the chart.
Forecast line: A continuous line is plotted to represent the estimated future price values.
Practical applications
Short-term Trading: identify repetitive market cycles to anticipate future movements.
Visual Decision-making: colored signals and labels make it easier to visualize potential profit or loss for each trade.
Advanced Customization: adjust the data length and colors to tailor the indicator to your strategies.
Limitations
Prediction price models have some limitations. Trading decisions should be made with caution, considering additional market factors and risk management strategies.
Segment RegressionAs an example of the descriptive power of Pine Script, this very short example traces a 'segment regression', a result not entirely obvious with so few lines of code, repositioning them when the previous inference moves away from the graph beyond the pre-set limit.
A trick used is to restart the new inference segment
- from the maximum reached in the previous trend, when positive (slope>0)
- from the minimum reached in the previous trend, when negative (slope<0)
The result can in my opinion be easily used to build strategies.
[Excalibur] Advanced Polynomial Regression Trend ChannelIt's been a long time coming... Regression channel enthusiasts, it's 'ultimately' here! Welcome to my Apophis page. But first, let me explain the origins of its attributed name blending both descriptive & engaging content with concise & technical topics...
EGYPTIAN ROOTED TALES:
Apophis (Greek) or Apep (Egyptian) was known by many cultures to be a mighty Egyptian archetype of chaos, darkness, and destruction. In ancient Egyptian mythology, Apophis was often depicted in the form of a fearsome menacing serpent, in those days, with an insatiable appetite for relentless malevolence. This dreaded entity was considered a formidable enemy and was also believed to appear as a giant serpent arising from the underworld.
Forever engaging in eternal battle, according to lore, Apophis' adversarial attributes represented the forces of disorder and anarchy clashing with the forces of order and harmony. This serpent's wickedly described figure was significantly symbolic of the disruptive, treacherous powers that Apophis embodied, those which threatened to plunge the perceivable archaic world into darkness. To the ancients, the legendary cyclical struggles against Apophis served as allegory reflecting on the macrocosm of the larger conflict between good and evil disparities that shaped early ancient civilization, much like the tree serpent.
One of Apophis’ mythological roots was immortally depicted on tomb stone. On one particular hieroglyphic wall tableau, in the second chamber of Inherkau’s tomb at Deir el-Medina, within the Theban Necropolis, portrays a mural of a serpent (Apep) under an edible fruit tree being slain in defeat. The species of snake depicted on various locations of tomb walls appears to me to bear a striking resemblance to the big eyed Echis pyramidum (Egyptian saw-scaled viper) native to regions of North Africa and the Middle East. It's a species of viper notoriously contributing to the most snake bite fatalities in the world still to this day; talk about a true harbinger of chaos incarnate. You do NOT want to cross paths with this asp in the dark of night, ever! Nor the other species of Echis found around Echid trees in the garden.
As we all know, fabled archaic storytelling can be misconstruing. Yet, these archaic serpent narratives still have echoes of significant notions and wisdom to learn from, especially in a modern technological society still rife with miscalculating deep snakes slithering about with intent to specifically plot disorder on national scales, and then profitably capitalize on it. Many deep black snakes are hiding in plain sight and under rocks. They do indeed speak and spell with forked tongues and malfeasance to the masses. I have great news. Tools now exist in the realms of AI combined with fractal programming circles to uncover these venomous viper mesh networks and investigatively monitor their subversive activities, so their days are surely numbered for... GAME OVER. Prepare to meet the doom you vain vipers have sought!
The arrival of the great and powerful international storm of the century has come, clothed in vindication. It's the only just way for the globe to clean house and move forward economically into the evolving herafter unobstructed by rampant evils and corruption. The foundations of future architectures are being established, and these nefarious obstacles MUST NOT hinder that path ahead.
With my former days of serpent wrangling being behind me, I now explore avenues of history, philosophy, programming, and mathematics, weaving them all into my daily routine. Now is the time to make some mathematical history unfold and get to the good and spicy stuff that you as the reader seek...
CALCULATING ON CHAOS:
Perhaps frightful characteristics of serpents (their maneuverability to adapt to any swervy situation) could be harnessed and channeled into a powerful tool for navigating the treacherous waters of data chaos. What if taming a monstrous beast of mayhem was not only possible, but fully achievable? Well, I think I have improved upon an approach to better tackle fractal chaos handling and observation within a modest PSv6 float environment without doubles. Finally, I've successfully turned my pet anaconda, Apophis, into a docile form of mathematical charting resilience beyond anything I have ever visually witnessed before. This novel work clearly deprecates ALL of my prior regression works by performing everything those delivered AND more, but it doesn't necessarily eliminate them into extinction.
INTRODUCTION:
Allow me to introduce Apophis! What you see showcased above is also referred to as 'Advanced Polynomial Regression Trend Channel' (APRTC) for technical minds. I would describe it as an avant-garde trend channel obtaining accurate polynomial approximations on market data with Pine v6.0. APRTC is a fractal following demystifier that I can only describe as being a signal trajectory tracking stalker manifesting as a data devouring demon. My full-fledged 'Excalibur' version of poly-regression swiftly captures undulating patterns present in market data with ease and at warp speed faster than you can blink. Now unchained, this is my rendering of polynomial wrath employing the "Immense Power of Pine".
By pushing techniques of regression to extremes, I am able to trace the serpentine trajectory of chaos up to a 50th order with 100s or 1000s of samples via "advanced polynomial regression" (APR), aka Apophis. This uniquely reactive trend channel method is designed to enhance the way we engage with the complex challenge of observably interpreting chaotic price behavior. While this is the end of the road for my revolutionary trend channel technology, that doesn't imply that future polynomial regression upgrades won't/might occur... There are a number of other supplementary concepts I have in my mind that could potentially prove useful eventually, who knows. However, for the moment, I feel it's wisest to monitor how accommodating APRTC is towards servers for the present time.
HISTORICAL ENDEAVORS:
Having wrangled countless wild serpents in my youth by the handfuls, tackling this was one multi-headed regression challenge temptation I couldn't resist. Besides, serpents in reality are more than often scared of us in the wild, so I assumed this shouldn't be too terribly hard. Wrong! It's been a complex struggle indeed. APRTC gave me many stinging bites for a LONG time. I had unknowingly opened Pandora's box of polynomials unprepared for what was to follow.
Long have I wrestled with Apophis throughout many nights for years with adversity, at last having arrived at a current grand solution and ultimately emerging victorious. Now, does the significance of the entitled name Apophis become more apparent at this point of reading? What you can now witness above is a very powerful blend of precision combined with maneuverability, concluding my dreamy expectations of a maximal experience with polynomial regression in TV charts. With all of my wizardry components finally assembled, Apophis genuinely is the most phenomenal indicator I ever devised in my life... as of yet.
How was this accomplished? By unlocking a deep understanding of the mathematical principles that govern regression, combined with an arsenal of mathemagical trickeries through sheer determination. I also spent an incredible amount of time flexing the unbendable 64bit float numerics to obtain a feasible order/degree of up to 50 polynomials or up to 4000 bars of regression (never simultaneously) on a labyrinth of samples. Lastly, what was needed was a pinch of mathematical pixie dust with a pleasant dose of Pine upgrades (lots of line re-drawings) that millions of other members can also utilize. Thank you so much, Pine developers, for once again turning meager proposed visions into materialized reality by leveraging the "Power of Pine" for the many!
DESCRIBING POLYNOMIAL REGRESSION:
APRTC is a visual guide for navigating noisy markets, providing both trajectory and structure through the power of mathematical modeling. Polynomial regression, especially at higher orders, exhibits obvious sidewinder/serpentine like characteristics. Even the channel extremities, on swift one second charts, resemble scales in motion with a pair of dashed exterior lines. This poly version presently yields the best quality of fit, providing an extreme "visual analysis" of your price action in high noise environments. The greater the order of the polynomial, the more pronounced the meandering regression characteristics become, as the algorithm strives to visually capture the fundamental fractal patterns most effectively.
Polynomial Regression in Action:
The medial line displays the core polynomial regression approximation in similarity to spinal backbones of serpents when following the movements of market data. Encasing the central structure, the channel's skin consists of enveloping lines having upper and lower extremes. To further enhance visualization, background fill colors distinguish the breadth between positive and negative territories of potential movement.
Additional internal dotted variability lines are available with multiple customizable settings to adjust dynamic dispersion, color, etc. One other exciting feature I added is the the ability to see the polynomial values with up to 50 (adjustable) decimal places if available. Witnessing Xⁿ values tapering near to 0.0 may indicate overfitting. Linear regression is available at order=1 and quadratic regression is invoked using order=2.
Information Criterion:
A toggleable label provides a multitude of information such as Bayesian Information Criterion (BIC), order, period, etc. BIC serves as an polynomial regression fit metric, with lesser values indicating a better balance between polynomial order adjustments, reflecting a more accurate fit in relation to the channel's girth. One downside of BIC values is their often large numerical values, making visual comparisons challenging, and then also their rare occurrence as negative values.
Furthermore, I formulated my own "EXPERIMENTAL" Simpler Information Criterion (SIC) fit metric, which seems to offer better visual interpretability when adjusting order settings on a selected regression period, especially on minuscule price numerics. Positive valued SIC numerics with lesser digits also reflect a preferred better fit during order adjustment, same as applying BIC principles of the minimum having a superior calulation tendency. I'll let members be the judge of deciding whether my SIC is actually a superior information criterion compared to BIC.
TECHNICAL INTERPRETATION and APPLICATION:
The Apophis indicator utilizes high-order polynomial regression, up to a maximum 50th order ability to deliver a nuanced, visual representation of complex market dynamics. I would caution against using upwards toward a 50th order, because opting for a 50th order polynomial is categorically speaking "wildly unsane" in real-world practice. As the polynomial degree increases from lesser orders, the regression line exhibits more pronounced curvature and undulations.
Visually analyzing the regression curve can provide insights into prevailing trends, as well as volatility regimes. For example, a gently sloping line may signal a steady directional trend, while a tightly curled oscillating curve may indicate heightened volatility and range-bound trading. Settings are rather straight forward, and comparable to my former "Quadratic Regression Trend Channel" efforts, although one torturous feature from QRTC is omitted due too computational complexity concerns.
Notice: Trial invite only access will not be granted for this indicator. Those who are familiar with recognizing what APRTC is, you will either want it or not, to add to your arsenal of trading approaches.
When available time provides itself, I will consider your inquiries, thoughts, and concepts presented below in the comments section, should you have any questions or comments regarding this indicator. When my indicators achieve more prevalent use by TV members , I may implement more ideas when they present themselves as worthy additions. Have a profitable future everyone!
RISK DISCLAIMER:
My scripts and indicators are specifically intended for informational and educational use only. This script uses historical data points to perform calculations to derive real-time calculations. They do not infer, indicate, or guarantee future results or performance.
By utilizing this script/indicator or any portion of it, you agree to accept 100% responsibly and liability for your investment or financial decisions, and I will not be held liable for your subjective analytic interpretations incurring sustained monetary losses. The opinions and information visual or otherwise provided by this script/indicator is not investment advice, nor does it constitute recommendation.
