BTC Parabolic Trend Lines v6 (jerikoo)

10 Ogo

📈 BTC Parabolic Trend Lines v6 - Power Law Regression Indicator
Description:

Advanced regression analysis tool that fits parabolic curves to Bitcoin's price history, revealing long-term growth patterns and future projections based on mathematical power laws.

This indicator implements three types of regression models optimized for Bitcoin's unique price behavior:
🎯 Key Features:

1. Power Law Regression (Recommended for BTC)

Fits the famous Bitcoin Power Law: Price = Offset + A × time^B
Captures BTC's diminishing growth rate over time
Provides the most accurate long-term fit with R² typically > 0.94

2. Multiple Regression Types

Power Law: Best for long-term BTC analysis
Exponential: For shorter timeframes and aggressive growth phases
Polynomial: Quadratic/cubic curves for alternative modeling

3. Dynamic Channel Bands

Upper band (red): Overvalued zone - potential resistance
Lower band (green): Undervalued zone - potential support
Adjustable deviation multipliers based on historical volatility

4. Starting Price Offset

Accounts for Bitcoin's non-zero starting price (~$5-10)
Provides more realistic lower bounds
Improves fit accuracy for early price data

📊 How to Use:

Settings:

Regression Length: 400 bars recommended for best fit
Starting Price Offset: 5-10 for BTC (it didn't start at $0)
Channel Deviation: 1.5 standard deviations default
Future Projection: Extends regression into future (100 bars default)

Interpretation:

Yellow line: Fair value according to the regression model
Above red band: Potentially overvalued (historical tops often here)
Below green band: Potentially undervalued (historical bottoms often here)
R² Value: Closer to 1 = better fit (>0.9 is excellent)

🔄 Timeframe Adaptability:

Automatically recalculates when switching timeframes
Each timeframe shows its own optimized regression
Works on all timeframes from daily to monthly

📈 Trading Applications:

Long-term Investment: Identify accumulation zones when price is below fair value
Cycle Analysis: Spot potential tops when price exceeds upper band
Risk Management: Use bands as dynamic support/resistance levels
Portfolio Allocation: Increase/decrease position based on valuation zones

⚙️ Technical Details:

Uses logarithmic price transformation for better BTC fitting
Implements least squares regression for coefficient calculation
RMSE-based channel bands adapt to volatility
Smooth polyline rendering for visual clarity

📝 Notes:

Best suited for BTC due to its unique power law characteristics
Longer regression periods (300-500 bars) provide more stable trends
The projection assumes historical patterns continue (not financial advice)
Works best on logarithmic price scale for visualization

🎨 Visual Indicators:

Background coloring: Red (overvalued) / Green (undervalued)
Statistics label: Shows R², equation, and current valuation
Smooth curves: No gaps or jumps at current date
Future projection: Seamlessly extends from current price

⚠️ Important:

This is a statistical analysis tool, not a prediction system. Bitcoin's price can deviate significantly from the regression line during bull/bear cycles. The power law provides a long-term growth framework, not short-term trading signals.

Version: 6.0 Author: Created with Pine Script v6 Best For: BTC long-term analysis, cycle identification, valuation assessment Timeframes: All (Daily to Monthly recommended) Markets: Optimized for Bitcoin, may work on other crypto with adjustments

10 Ogo

Nota Keluaran

## 📈 BTC Parabolic Trend Lines v6 - Power Law Regression Indicator

### Description:

**Advanced regression analysis tool that fits parabolic curves to Bitcoin's price history, revealing long-term growth patterns and future projections based on mathematical power laws.**

This indicator implements three types of regression models optimized for Bitcoin's unique price behavior:

### 🎯 Key Features:

**1. Power Law Regression (Recommended for BTC)**
- Fits the famous Bitcoin Power Law: Price = Offset + A × time^B
- Captures BTC's diminishing growth rate over time
- Provides the most accurate long-term fit with R² typically > 0.94

**2. Multiple Regression Types**
- **Power Law**: Best for long-term BTC analysis
- **Exponential**: For shorter timeframes and aggressive growth phases
- **Polynomial**: Quadratic/cubic curves for alternative modeling

**3. Dynamic Channel Bands**
- Upper band (red): Overvalued zone - potential resistance
- Lower band (green): Undervalued zone - potential support
- Adjustable deviation multipliers based on historical volatility

**4. Starting Price Offset**
- Accounts for Bitcoin's non-zero starting price (~$5-10)
- Provides more realistic lower bounds
- Improves fit accuracy for early price data

### 📊 How to Use:

**Settings:**
- **Regression Length**: 400 bars recommended for best fit
- **Starting Price Offset**: 5-10 for BTC (it didn't start at $0)
- **Channel Deviation**: 1.5 standard deviations default
- **Future Projection**: Extends regression into future (100 bars default)

**Interpretation:**
- **Yellow line**: Fair value according to the regression model
- **Above red band**: Potentially overvalued (historical tops often here)
- **Below green band**: Potentially undervalued (historical bottoms often here)
- **R² Value**: Closer to 1 = better fit (>0.9 is excellent)

### 🔄 Timeframe Adaptability:
- Automatically recalculates when switching timeframes
- Each timeframe shows its own optimized regression
- Works on all timeframes from daily to monthly

### 📈 Trading Applications:

1. **Long-term Investment**: Identify accumulation zones when price is below fair value
2. **Cycle Analysis**: Spot potential tops when price exceeds upper band
3. **Risk Management**: Use bands as dynamic support/resistance levels
4. **Portfolio Allocation**: Increase/decrease position based on valuation zones

### ⚙️ Technical Details:
- Uses logarithmic price transformation for better BTC fitting
- Implements least squares regression for coefficient calculation
- RMSE-based channel bands adapt to volatility
- Smooth polyline rendering for visual clarity

### 📝 Notes:
- Best suited for BTC due to its unique power law characteristics
- Longer regression periods (300-500 bars) provide more stable trends
- The projection assumes historical patterns continue (not financial advice)
- Works best on logarithmic price scale for visualization

### 🎨 Visual Indicators:
- **Background coloring**: Red (overvalued) / Green (undervalued)
- **Statistics label**: Shows R², equation, and current valuation
- **Smooth curves**: No gaps or jumps at current date
- **Future projection**: Seamlessly extends from current price

### ⚠️ Important:
This is a statistical analysis tool, not a prediction system. Bitcoin's price can deviate significantly from the regression line during bull/bear cycles. The power law provides a long-term growth framework, not short-term trading signals.

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**Version**: 6.0
**Author**: Created with Pine Script v6
**Best For**: BTC long-term analysis, cycle identification, valuation assessment
**Timeframes**: All (Daily to Monthly recommended)
**Markets**: Optimized for Bitcoin, may work on other crypto with adjustments