OPEN-SOURCE SCRIPT
Auto-Fit Growth Trendline

# **Theoretical Algorithmic Principles of the Auto-Fit Growth Trendline (AFGT)**
## **🎯 What Does This Algorithm Do?**
The Auto-Fit Growth Trendline is an advanced technical analysis system that **automates the identification of long-term growth trends** and **projects future price levels** based on historical cyclical patterns.
### **Primary Functionality:**
- **Automatically detects** the most significant lows in regular periods (monthly, quarterly, semi-annually, annually)
- **Constructs a dynamic trendline** that connects these historical lows
- **Projects the trend into the future** with high mathematical precision
- **Generates Fibonacci bands** that act as dynamic support and resistance levels
- **Automatically adapts** to different timeframes and market conditions
### **Strategic Purpose:**
The algorithm is designed to identify **fundamental value zones** where price has historically found support, enabling traders to:
- Identify optimal entry points for long positions
- Establish realistic price targets based on mathematical projections
- Recognize dynamic support and resistance levels
- Anticipate long-term price movements
---
## **🧮 Core Mathematical Foundations**
### **Adaptive Temporal Segmentation Theory**
The algorithm is based on **dynamic temporal partition theory**, where time is divided into mathematically coherent uniform intervals. It uses modular transformations to create bijective mappings between continuous timestamps and discrete periods, ensuring each temporal point belongs uniquely to a specific period.
**What does this achieve?** It allows the algorithm to automatically identify natural market cycles (annual, quarterly, etc.) without manual intervention, adapting to the inherent periodicity of each asset.
The temporal mapping function implements a **discrete affine transformation** that normalizes different frequencies (monthly, quarterly, semi-annual, annual) to a space of unique identifiers, enabling consistent cross-temporal comparative analysis.
---
## **📊 Local Extrema Detection Theory**
### **Multi-Point Retrospective Validation Principle**
Local minima detection is founded on **relative extrema theory with sliding window**. Instead of using a simple minimum finder, it implements a cross-validation system that examines the persistence of the extremum across multiple historical periods.
**What problem does this solve?** It eliminates false minima caused by temporal volatility, identifying only those points that represent true historical support levels with statistical significance.
This approach is based on the **statistical confirmation principle**, where a minimum is only considered valid if it maintains its extremum condition during a defined observation period, significantly reducing false positives caused by transitory volatility.
---
## **🔬 Robust Interpolation Theory with Outlier Control**
### **Contextual Adaptive Interpolation Model**
The mathematical core uses **piecewise linear interpolation with adaptive outlier correction**. The key innovation lies in implementing a **contextual anomaly detector** that identifies not only absolute extreme values, but relative deviations to the local context.
**Why is this important?** Financial markets contain extreme events (crashes, bubbles) that can distort projections. This system identifies and appropriately weights them without completely eliminating them, preserving directional information while attenuating distortions.
### **Implicit Bayesian Smoothing Algorithm**
When an outlier is detected (deviation >300% of local average), the system applies a **simplified Kalman filter** that combines the current observation with a local trend estimation, using a weight factor that preserves directional information while attenuating extreme fluctuations.
---
## **📈 Stabilized Extrapolation Theory**
### **Exponential Growth Model with Dampening**
Extrapolation is based on a **modified exponential growth model with progressive dampening**. It uses multiple historical points to calculate local growth ratios, implements statistical filtering to eliminate outliers, and applies a dampening factor that increases with extrapolation distance.
**What advantage does this offer?** Long-term projections in finance tend to be exponentially unrealistic. This system maintains short-to-medium term accuracy while converging toward realistic long-term projections, avoiding the typical "exponential explosions" of other methods.
### **Asymptotic Convergence Principle**
For long-term projections, the algorithm implements **controlled asymptotic convergence**, where growth ratios gradually converge toward pre-established limits, avoiding unrealistic exponential projections while preserving short-to-medium term accuracy.
---
## **🌟 Dynamic Fibonacci Projection Theory**
### **Continuous Proportional Scaling Model**
Fibonacci bands are constructed through **uniform proportional scaling** of the base curve, where each level represents a linear transformation of the main curve by a constant factor derived from the Fibonacci sequence.
**What is its practical utility?** It provides dynamic resistance and support levels that move with the trend, offering price targets and profit-taking points that automatically adapt to market evolution.
### **Topological Preservation Principle**
The system maintains the **topological properties** of the base curve in all Fibonacci projections, ensuring that spatial and temporal relationships are consistently preserved across all resistance/support levels.
---
## **⚡ Adaptive Computational Optimization**
### **Multi-Scale Resolution Theory**
It implements **automatic multi-resolution analysis** where data granularity is dynamically adjusted according to the analysis timeframe. It uses the **adaptive Nyquist principle** to optimize the signal-to-noise ratio according to the temporal observation scale.
**Why is this necessary?** Different timeframes require different levels of detail. A 1-minute chart needs more granularity than a monthly one. This system automatically optimizes resolution for each case.
### **Adaptive Density Algorithm**
Calculation point density is optimized through **adaptive sampling theory**, where calculation frequency is adjusted according to local trend curvature and analysis timeframe, balancing visual precision with computational efficiency.
---
## **🛡️ Robustness and Fault Tolerance**
### **Graceful Degradation Theory**
The system implements **multi-level graceful degradation**, where under error conditions or insufficient data, the algorithm progressively falls back to simpler but reliable methods, maintaining basic functionality under any condition.
**What does this guarantee?** That the indicator functions consistently even with incomplete data, new symbols with limited history, or extreme market conditions.
### **State Consistency Principle**
It uses **mathematical invariants** to guarantee that the algorithm's internal state remains consistent between executions, implementing consistency checks that validate data structure integrity in each iteration.
---
## **🔍 Key Theoretical Innovations**
### **A. Contextual vs. Absolute Outlier Detection**
It revolutionizes traditional outlier detection by considering not only the absolute magnitude of deviations, but their relative significance within the local context of the time series.
**Practical impact:** It distinguishes between legitimate market movements and technical anomalies, preserving important events like breakouts while filtering noise.
### **B. Extrapolation with Weighted Historical Memory**
It implements a memory system that weights different historical periods according to their relevance for current prediction, creating projections more adaptable to market regime changes.
**Competitive advantage:** It automatically adapts to fundamental changes in asset dynamics without requiring manual recalibration.
### **C. Automatic Multi-Timeframe Adaptation**
It develops an automatic temporal resolution selection system that optimizes signal extraction according to the intrinsic characteristics of the analysis timeframe.
**Result:** A single indicator that functions optimally from 1-minute to monthly charts without manual adjustments.
### **D. Intelligent Asymptotic Convergence**
It introduces the concept of controlled asymptotic convergence in financial extrapolations, where long-term projections converge toward realistic limits based on historical fundamentals.
**Added value:** Mathematically sound long-term projections that avoid the unrealistic extremes typical of other extrapolation methods.
---
## **📊 Complexity and Scalability Theory**
### **Optimized Linear Complexity Model**
The algorithm maintains **linear computational complexity** O(n) in the number of historical data points, guaranteeing scalability for extensive time series analysis without performance degradation.
### **Temporal Locality Principle**
It implements **temporal locality**, where the most expensive operations are concentrated in the most relevant temporal regions (recent periods and near projections), optimizing computational resource usage.
---
## **🎯 Convergence and Stability**
### **Probabilistic Convergence Theory**
The system guarantees **probabilistic convergence** toward the real underlying trend, where projection accuracy increases with the amount of available historical data, following **law of large numbers** principles.
**Practical implication:** The more history an asset has, the more accurate the algorithm's projections will be.
### **Guaranteed Numerical Stability**
It implements **intrinsic numerical stability** through the use of robust floating-point arithmetic and validations that prevent overflow, underflow, and numerical error propagation.
**Result:** Reliable operation even with extreme-priced assets (from satoshis to thousand-dollar stocks).
---
## **💼 Comprehensive Practical Application**
**The algorithm functions as a "financial GPS"** that:
1. **Identifies where we've been** (significant historical lows)
2. **Determines where we are** (current position relative to the trend)
3. **Projects where we're going** (future trend with specific price levels)
4. **Provides alternative routes** (Fibonacci bands as alternative targets)
This theoretical framework represents an innovative synthesis of time series analysis, approximation theory, and computational optimization, specifically designed for long-term financial trend analysis with robust and mathematically grounded projections.
## **🎯 What Does This Algorithm Do?**
The Auto-Fit Growth Trendline is an advanced technical analysis system that **automates the identification of long-term growth trends** and **projects future price levels** based on historical cyclical patterns.
### **Primary Functionality:**
- **Automatically detects** the most significant lows in regular periods (monthly, quarterly, semi-annually, annually)
- **Constructs a dynamic trendline** that connects these historical lows
- **Projects the trend into the future** with high mathematical precision
- **Generates Fibonacci bands** that act as dynamic support and resistance levels
- **Automatically adapts** to different timeframes and market conditions
### **Strategic Purpose:**
The algorithm is designed to identify **fundamental value zones** where price has historically found support, enabling traders to:
- Identify optimal entry points for long positions
- Establish realistic price targets based on mathematical projections
- Recognize dynamic support and resistance levels
- Anticipate long-term price movements
---
## **🧮 Core Mathematical Foundations**
### **Adaptive Temporal Segmentation Theory**
The algorithm is based on **dynamic temporal partition theory**, where time is divided into mathematically coherent uniform intervals. It uses modular transformations to create bijective mappings between continuous timestamps and discrete periods, ensuring each temporal point belongs uniquely to a specific period.
**What does this achieve?** It allows the algorithm to automatically identify natural market cycles (annual, quarterly, etc.) without manual intervention, adapting to the inherent periodicity of each asset.
The temporal mapping function implements a **discrete affine transformation** that normalizes different frequencies (monthly, quarterly, semi-annual, annual) to a space of unique identifiers, enabling consistent cross-temporal comparative analysis.
---
## **📊 Local Extrema Detection Theory**
### **Multi-Point Retrospective Validation Principle**
Local minima detection is founded on **relative extrema theory with sliding window**. Instead of using a simple minimum finder, it implements a cross-validation system that examines the persistence of the extremum across multiple historical periods.
**What problem does this solve?** It eliminates false minima caused by temporal volatility, identifying only those points that represent true historical support levels with statistical significance.
This approach is based on the **statistical confirmation principle**, where a minimum is only considered valid if it maintains its extremum condition during a defined observation period, significantly reducing false positives caused by transitory volatility.
---
## **🔬 Robust Interpolation Theory with Outlier Control**
### **Contextual Adaptive Interpolation Model**
The mathematical core uses **piecewise linear interpolation with adaptive outlier correction**. The key innovation lies in implementing a **contextual anomaly detector** that identifies not only absolute extreme values, but relative deviations to the local context.
**Why is this important?** Financial markets contain extreme events (crashes, bubbles) that can distort projections. This system identifies and appropriately weights them without completely eliminating them, preserving directional information while attenuating distortions.
### **Implicit Bayesian Smoothing Algorithm**
When an outlier is detected (deviation >300% of local average), the system applies a **simplified Kalman filter** that combines the current observation with a local trend estimation, using a weight factor that preserves directional information while attenuating extreme fluctuations.
---
## **📈 Stabilized Extrapolation Theory**
### **Exponential Growth Model with Dampening**
Extrapolation is based on a **modified exponential growth model with progressive dampening**. It uses multiple historical points to calculate local growth ratios, implements statistical filtering to eliminate outliers, and applies a dampening factor that increases with extrapolation distance.
**What advantage does this offer?** Long-term projections in finance tend to be exponentially unrealistic. This system maintains short-to-medium term accuracy while converging toward realistic long-term projections, avoiding the typical "exponential explosions" of other methods.
### **Asymptotic Convergence Principle**
For long-term projections, the algorithm implements **controlled asymptotic convergence**, where growth ratios gradually converge toward pre-established limits, avoiding unrealistic exponential projections while preserving short-to-medium term accuracy.
---
## **🌟 Dynamic Fibonacci Projection Theory**
### **Continuous Proportional Scaling Model**
Fibonacci bands are constructed through **uniform proportional scaling** of the base curve, where each level represents a linear transformation of the main curve by a constant factor derived from the Fibonacci sequence.
**What is its practical utility?** It provides dynamic resistance and support levels that move with the trend, offering price targets and profit-taking points that automatically adapt to market evolution.
### **Topological Preservation Principle**
The system maintains the **topological properties** of the base curve in all Fibonacci projections, ensuring that spatial and temporal relationships are consistently preserved across all resistance/support levels.
---
## **⚡ Adaptive Computational Optimization**
### **Multi-Scale Resolution Theory**
It implements **automatic multi-resolution analysis** where data granularity is dynamically adjusted according to the analysis timeframe. It uses the **adaptive Nyquist principle** to optimize the signal-to-noise ratio according to the temporal observation scale.
**Why is this necessary?** Different timeframes require different levels of detail. A 1-minute chart needs more granularity than a monthly one. This system automatically optimizes resolution for each case.
### **Adaptive Density Algorithm**
Calculation point density is optimized through **adaptive sampling theory**, where calculation frequency is adjusted according to local trend curvature and analysis timeframe, balancing visual precision with computational efficiency.
---
## **🛡️ Robustness and Fault Tolerance**
### **Graceful Degradation Theory**
The system implements **multi-level graceful degradation**, where under error conditions or insufficient data, the algorithm progressively falls back to simpler but reliable methods, maintaining basic functionality under any condition.
**What does this guarantee?** That the indicator functions consistently even with incomplete data, new symbols with limited history, or extreme market conditions.
### **State Consistency Principle**
It uses **mathematical invariants** to guarantee that the algorithm's internal state remains consistent between executions, implementing consistency checks that validate data structure integrity in each iteration.
---
## **🔍 Key Theoretical Innovations**
### **A. Contextual vs. Absolute Outlier Detection**
It revolutionizes traditional outlier detection by considering not only the absolute magnitude of deviations, but their relative significance within the local context of the time series.
**Practical impact:** It distinguishes between legitimate market movements and technical anomalies, preserving important events like breakouts while filtering noise.
### **B. Extrapolation with Weighted Historical Memory**
It implements a memory system that weights different historical periods according to their relevance for current prediction, creating projections more adaptable to market regime changes.
**Competitive advantage:** It automatically adapts to fundamental changes in asset dynamics without requiring manual recalibration.
### **C. Automatic Multi-Timeframe Adaptation**
It develops an automatic temporal resolution selection system that optimizes signal extraction according to the intrinsic characteristics of the analysis timeframe.
**Result:** A single indicator that functions optimally from 1-minute to monthly charts without manual adjustments.
### **D. Intelligent Asymptotic Convergence**
It introduces the concept of controlled asymptotic convergence in financial extrapolations, where long-term projections converge toward realistic limits based on historical fundamentals.
**Added value:** Mathematically sound long-term projections that avoid the unrealistic extremes typical of other extrapolation methods.
---
## **📊 Complexity and Scalability Theory**
### **Optimized Linear Complexity Model**
The algorithm maintains **linear computational complexity** O(n) in the number of historical data points, guaranteeing scalability for extensive time series analysis without performance degradation.
### **Temporal Locality Principle**
It implements **temporal locality**, where the most expensive operations are concentrated in the most relevant temporal regions (recent periods and near projections), optimizing computational resource usage.
---
## **🎯 Convergence and Stability**
### **Probabilistic Convergence Theory**
The system guarantees **probabilistic convergence** toward the real underlying trend, where projection accuracy increases with the amount of available historical data, following **law of large numbers** principles.
**Practical implication:** The more history an asset has, the more accurate the algorithm's projections will be.
### **Guaranteed Numerical Stability**
It implements **intrinsic numerical stability** through the use of robust floating-point arithmetic and validations that prevent overflow, underflow, and numerical error propagation.
**Result:** Reliable operation even with extreme-priced assets (from satoshis to thousand-dollar stocks).
---
## **💼 Comprehensive Practical Application**
**The algorithm functions as a "financial GPS"** that:
1. **Identifies where we've been** (significant historical lows)
2. **Determines where we are** (current position relative to the trend)
3. **Projects where we're going** (future trend with specific price levels)
4. **Provides alternative routes** (Fibonacci bands as alternative targets)
This theoretical framework represents an innovative synthesis of time series analysis, approximation theory, and computational optimization, specifically designed for long-term financial trend analysis with robust and mathematically grounded projections.
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Penafian
Maklumat dan penerbitan adalah tidak dimaksudkan untuk menjadi, dan tidak membentuk, nasihat untuk kewangan, pelaburan, perdagangan dan jenis-jenis lain atau cadangan yang dibekalkan atau disahkan oleh TradingView. Baca dengan lebih lanjut di Terma Penggunaan.
Skrip sumber terbuka
Dalam semangat sebenar TradingView, pencipta skrip ini telah menjadikannya sumber terbuka supaya pedagang dapat menilai dan mengesahkan kefungsiannya. Terima kasih kepada penulis! Walaupun anda boleh menggunakannya secara percuma, ingat bahawa menerbitkan semula kod ini adalah tertakluk kepada Peraturan Dalaman kami.
Penafian
Maklumat dan penerbitan adalah tidak dimaksudkan untuk menjadi, dan tidak membentuk, nasihat untuk kewangan, pelaburan, perdagangan dan jenis-jenis lain atau cadangan yang dibekalkan atau disahkan oleh TradingView. Baca dengan lebih lanjut di Terma Penggunaan.