Polynomial Regression Band

What is a Polynomial Regression Band?

A polynomial regression band is a curved channel built by fitting a polynomial to recent prices with least squares, then offsetting the fitted curve above and below by a volatility measure, usually a multiple of the fit's standard deviation or root-mean-square error. Where a linear-regression channel forces a straight line through the window, a polynomial of degree two or higher can bend with the data, so the channel follows curved trends and rounded turns more closely.

Two versions exist. The full-curve version draws the fitted polynomial across the whole lookback and refits on every new bar, so the historical segment moves as data arrives. The end-point version keeps only the newest fitted value per bar, producing a causal line that never redraws (the same idea behind the LSMA, which is the end point of a linear fit). Higher degrees track price more tightly but fit noise and behave erratically near the window's edges, so extrapolating the curve forward is unreliable.

How traders use it

• As curved dynamic support and resistance: pullbacks toward the lower band in a rising fit, or the upper band in a falling one, are watched for reactions, with band width scaling to how loosely price sits around the curve.
• As a mean-reversion frame inside the window: price stretched to an outer band is treated as extended relative to the fitted curve, a context read rather than a standalone signal, since strong trends can ride a band for many bars.
• As a smoother trend proxy: the slope of the end-point line gives a direction filter that picks up curvature sooner than a straight regression line, at the cost of more noise sensitivity as the degree rises.