Three-zone price channel from quadratic smoothing

A timing envelope, not a travel forecast

The channel is framed as a timing envelope for entering and exiting a security. It is not a device that projects how far price will travel.

The price channel is the pair of comfort-scaled bounds traced through time. It turns the forecast into an objective envelope instead of a point prediction.

A quadratic forecast with changing coefficients

Construction begins with a quadratic time-series projection whose coefficients represent trend velocity and acceleration and are allowed to change rather than stay fixed.

The quadratic forecast is a local polynomial path. Its coefficients stand for estimated price level, velocity, and acceleration at the moment of projection.

Level, velocity, and acceleration are updated recursively with analyst-chosen smoothing constants. Exponential smoothing is recursive weighting of ordered observations that refreshes level, velocity, acceleration, and error variance, giving more influence to recent prints.

Comfort-scaled expected error

Upper and lower bounds are formed by adding and subtracting a comfort-scaled expected-error term from the forecast line.

Expected error is the tracked gap between realized price and the model’s expected outcome. It is used to size the envelope rather than to revise a causal story.

In the illustrated construction, expected error is obtained by exponentially smoothing the squared differences between realized prices and the model’s expected outcomes.

The comfort factor is a risk-tolerance scalar applied to the expected-error estimate. It sets how far the upper and lower bounds sit from the forecast line. A comfort factor of 1 is presented as equivalent to one standard deviation on each side of the forecast, matching a conventional Student t-style interval around the best estimate.

Once coefficients, forecast horizon, and comfort factor are fixed, the channel is applied uniformly by formula. Freehand envelopes are treated as subjective and easily widened by a few large deviations.

Three regions from an envelope exit

Price leaving the envelope is used to mark a break in the assumed trend and to partition the chart into deteriorating, neutral, and improving regions.

The deteriorating region is the area below the lower bound, read as evidence that the assumed trend has weakened. The neutral region is the interior of the channel, read as consistent with continuation of the estimated trend. The improving region is the area above the upper bound, read as evidence that price is outrunning the prior trend.

Contrast with a moving-average cross

The channel and a moving average both generate signals from price crossing a computed line. The channel is designed to extrapolate and to place greater weight on recent observations.

A moving average, in this comparison, is a non-extrapolating average of past prices used as a baseline for crossing rules.

Editorial: the anticipatory three-zone channel is the object offered for checking. The moving-average cross does not extrapolate.

When the smoother is a poor fit

The quadratic smoother is described as unsuitable while a security is building a base, or while trend change is so small that the channel merely tracks price.

A worked daily initialization

A worked daily example initializes the smoothing constants and the error-smoothing constant at 0.5 and the comfort factor at 1. It then forms the next day’s bounds from a one-step forecast plus or minus the comfort-scaled error term.