Isotonic Regression [LuxAlgo]

The Isotonic Regression indicator provides a monotonic fit to price data, ensuring the resulting line is either non-decreasing or non-increasing over a specified lookback period. This tool is particularly useful for identifying underlying trends and significant price plateaus without the lagging or "overshooting" common in standard moving averages or linear regressions.

Note: This indicator calculates its values based on a historical lookback window, which means the regression line will repaint as new bars are added and the window shifts.

🔶 USAGE

Isotonic regression is used to find the best-fitting line to a set of data points under the constraint that the line must move in a specific direction (always up or always down). This creates a "staircase" effect where the model alternates between trending segments and flat plateaus.

🔹 Direction Modes

The indicator offers three ways to determine the fit direction:

• Auto: Automatically detects the trend by comparing the start and end prices of the lookback period. If the end price is higher, it fits a non-decreasing line; otherwise, it fits a non-increasing line.
  
• Non-Decreasing: Forces the fit to only move upwards or stay flat, ideal for analyzing bullish structures.
  
• Non-Increasing: Forces the fit to only move downwards or stay flat, ideal for analyzing bearish structures.

🔹 Flat Period Extensions

One of the most powerful features of isotonic regression is the identification of "blocks" or price levels where the trend pauses. When the duration of such a plateau exceeds the Flat Period Threshold, the indicator extends a dashed horizontal line to the current bar, highlighting potential support or resistance levels derived from the regression model.

🔶 DETAILS

The script implements the Pool Adjacent Violators Algorithm (PAVA), which is the standard method for computing isotonic regression.

The algorithm works by partitioning the data into "blocks." If a subsequent data point violates the monotonicity constraint (e.g., price drops in a "non-decreasing" fit), the algorithm pools the current block with the previous one and calculates a weighted average. This process repeats until the entire sequence is monotonic.

For performance efficiency, the indicator utilizes the

polyline.new()

function to render the regression line as a single continuous object rather than hundreds of individual line segments.

🔶 SETTINGS

• Lookback Length: The number of bars used to calculate the isotonic fit.
  
• Source: The price data used for the calculation (default is Close).
  
• Direction: Sets the monotonicity constraint (Auto, Non-Decreasing, or Non-Increasing).
  
• Flat Period Threshold: The minimum number of bars a price plateau must last to be highlighted with an extension line.

🔹 Style

• Fit Bullish/Bearish: Colors for the regression line based on the detected trend.
  
• Fit Style/Width: Controls the visual representation (Solid, Dashed, Dotted) and thickness of the main regression line.
  
• Ext Bullish/Bearish: Colors for the flat period extension levels.
  
• Ext Style/Width: Controls the visual representation and thickness of the plateau extensions.