Polynomial Bands

Polynomial Bands apply a second-degree least-squares regression model to estimate the underlying non-linear trend of the price series. Over the selected lookback window, the indicator computes the quadratic polynomial

y(x) = A + Bx + Cx^2

and evaluates this function at the most recent bar. This value serves as the Base Line. It represents the fitted trend at the current location within the window.

After fitting the polynomial, the indicator calculates residuals by measuring the difference between observed prices and the regression curve. The sample variance of these residuals provides an estimate of dispersion around the fitted polynomial. The square root of this variance is used as the volatility measure for generating symmetric envelopes around the Base Line at multiples of the standard deviation.

The resulting bands represent regions of statistically expected deviation from the underlying quadratic trend. Narrow bands correspond to stable adherence to the modeled curve, while wide bands reflect increased irregularity or volatility.