Polynomial Regression Bands

#What you see

Three lines on the price chart: the regression line (Line Color), a translucent green upper band and a translucent red lower band. Each point comes from its own fit over the candles up to that point, so later candles do not redraw earlier values. With Show Window Curves on, ChartRider also draws the complete fitted curve and its bands across the window of the candle under the crosshair, and puts a dot on the most recent candle in that window whose high was above, or whose low was below, the curve's band.

#How it is calculated

For every candle, with N = Regression Period and k = Band width:

1. Fit y = a·x² + b·x + c by least squares to the last N closes at x = 0 to N − 1; with Linear Regression on, fit y = b·x + c.
2. regression is the fitted curve at the newest candle (x = N − 1).
3. σ = √(sum of (close − fit)² / N), the spread of the closes around the curve.
4. upper = regression + k × σ and lower = regression − k × σ.
5. slope is the change of the curve across the window relative to its newest value: (newest − oldest) / newest.
6. bend is the curvature from 0 to 1: |a| × (N − 1)² divided by the price range of the curve, compressed with x / (x + 0.15). 0 is a straight line (always with linear regression), values near 1 a strongly arched curve.

With Time Frame Multiplier above 1, the candles are first combined into a higher timeframe (chart timeframe × multiplier, aligned to UTC).

#How to read it

• The regression line is a smoothed trend estimate that bends with price, unlike a straight regression channel.
• Closes outside the bands are stretched relative to the window's trend: candidates for mean reversion in ranges, or signs of acceleration in breakouts.
• A rising bend while slope flattens hints that the curve is turning.

#Using it in strategies

Outputs: regression, upper, lower, slope and bend. In the Trade Setup, "Compare" a band with the price, e.g. lower above the price for a close below the lower band; "Price vs line" on regression is a trend filter. With a multiplier, a value only counts once its higher-timeframe candle has closed. WickScript has no built-in function for it; use use indicator "PolyReg" with period 150, periodBand 2 as pr and read pr.upper, pr.lower and the other outputs.

#Settings

Open the settings with the slider icon next to the indicator (Indicators, F3). Numeric settings can be swept as Step 1 / Step 2 parameters when you run a strategy.

#Inputs

#Styles

#Outputs

These values can be used in Trade Setup triggers, filters and exits (see Trade Setup) and in WickScript.

#Use in WickScript

use indicator creates this indicator inside a script, with settings by their ID. Each output is a field of the name after as. See WickScript indicators.

wickscript 1
indicator "Polynomial Regression Bands from the list" on chart
use indicator "PolyReg" with period 150 as myPolyreg
show myPolyreg.regression as line "regression"