Polynomial Regression Keltner Channel [ChartPrime]

Polynomial Regression Keltner Channel

⯁ OVERVIEW
The Polynomial Regression Keltner Channel [ChartPrime] indicator is an advanced technical analysis tool that combines polynomial regression with dynamic Keltner Channels. This indicator provides traders with a sophisticated method for trend analysis, volatility assessment, and identifying potential overbought and oversold conditions.

◆ KEY FEATURES

• Polynomial Regression: Uses polynomial regression for trend analysis and channel basis calculation.
  
  
• Dynamic Keltner Channels: Implements Keltner Channels with adaptive volatility-based bands.
  
  
• Overbought/Oversold Detection: Provides visual cues for potential overbought and oversold market conditions.
  
• Trend Identification: Offers clear trend direction signals and change indicators.
  
• Multiple Band Levels: Displays four levels of upper and lower bands for detailed market structure analysis.
  
• Customizable Visualization: Allows toggling of additional indicator lines and signals for enhanced chart analysis.
  
  
  

◆ FUNCTIONALITY DETAILS

⬥ Polynomial Regression Calculation:

• Implements a custom polynomial regression function for trend analysis.
  
• Serves as the basis for the Keltner Channel, providing a smoothed centerline.
  

  //@function Calculates polynomial regression
  //@param src (series float) Source price series
  //@param length (int) Lookback period
  //@returns (float) Polynomial regression value for the current bar
  polynomial_regression(src, length) =>
      sumX = 0.0
      sumY = 0.0
      sumXY = 0.0
      sumX2 = 0.0
      sumX3 = 0.0
      sumX4 = 0.0
      sumX2Y = 0.0
      n = float(length)
  
      for i = 0 to n - 1
          x = float(i)
          y = src
          sumX   += x
          sumY   += y
          sumXY  += x * y
          sumX2  += x * x
          sumX3  += x * x * x
          sumX4  += x * x * x * x
          sumX2Y += x * x * y
      
      slope = (n * sumXY - sumX * sumY) / (n * sumX2 - sumX * sumX)
      intercept = (sumY - slope * sumX) / n
      n - 1 * slope + intercept

⬥ Dynamic Keltner Channel Bands:

• Calculates ATR-based volatility for dynamic band width adjustment.
  
• Uses a base multiplier and adaptive volatility factor for flexible band calculation.
  
• Generates four levels of upper and lower bands for detailed market structure analysis.
  

  atr     = ta.atr(length)
  atr_sma = ta.sma(atr, 10)
  
  // Calculate Keltner Channel Bands
  dynamicMultiplier  = (1 + (atr / atr_sma)) * baseATRMultiplier
  volatility_basis   = (1 + (atr / atr_sma)) * dynamicMultiplier * atr

⬥ Overbought/Oversold Indicator line and Trend Line:

• Calculates an OB/OS value based on the price position relative to the innermost bands.
  
• Provides visual representation through color gradients and optional signal markers.
  
• Determines trend direction based on the polynomial regression line movement.
  
• Generates signals for trend changes, overbought/oversold conditions, and band crossovers.
  

◆ USAGE

• Trend Analysis: Use the color and direction of the basis line to identify overall trend direction.
  
• Volatility Assessment: The width and expansion/contraction of the bands indicate market volatility.
  
• Support/Resistance Levels: Multiple band levels can serve as potential support and resistance areas.
  
• Overbought/Oversold Trading: Utilize OB/OS signals for potential reversal or pullback trades.
  
• Breakout Detection: Monitor price crossovers of the outermost bands for potential breakout trades.
  

⯁ USER INPUTS

• Length: Sets the lookback period for calculations (default: 100).
  
• Source: Defines the price data used for calculations (default: HLC3).
  
• Base ATR Multiplier: Adjusts the base width of the Keltner Channels (default: 0.1).
  
• Indicator Lines: Toggle to show additional indicator lines and signals (default: false).
  

⯁ TECHNICAL NOTES

• Implements a custom polynomial regression function for efficient trend calculation.
  
• Uses dynamic ATR-based volatility adjustment for adaptive channel width.
  
• Employs color gradients and opacity levels for intuitive visual representation of market conditions.
  
• Utilizes Pine Script's plotchar function for efficient rendering of signals and heatmaps.
  

The Polynomial Regression Keltner Channel [ChartPrime] indicator offers traders a sophisticated tool for trend analysis, volatility assessment, and trade signal generation. By combining polynomial regression with dynamic Keltner Channels, it provides a comprehensive view of market structure and potential trading opportunities. The indicator's adaptability to different market conditions and its customizable nature make it suitable for various trading styles and timeframes.