Range-dimension adaptive exponential filter

What the construction does

This archive article restates a historical workflow for an adaptive moving average. That name means a smoother whose blending weight changes with a measured market-state diagnostic instead of staying a fixed constant. The update is exponential smoothing, a one-step recurrence that mixes the newest observation with the previous output using a coefficient between zero and one.

Default observation and even lookback

The default observation fed to the filter is the midpoint of each bar's high and low. The construction uses an even lookback, meaning an even bar count that sets both the paired half-windows used for the range measures and the warm-up before the recurrence is applied. A supplied default for that length is 16 bars.

Range measures and range-based dimension

High-low spans are measured on the first half-window, the second half-window, and the full lookback, then scaled by the corresponding window length. A range-based dimension is a log-ratio of half-window and full-window high-low spans that rises when the path looks more space-filling over the lookback. The estimate is formed as the log of the sum of the two half-window range measures minus the log of the full-window range measure, divided by the log of 2, and only when all three range measures are positive.

Smoothing coefficient and recursive output

The smoothing coefficient is the weight applied to the current observation in the exponential update. It is derived from the dimension estimate by exponentiating -4.6 times the dimension estimate minus one, then forced to stay inside the closed interval from 0.01 to 1. After warm-up, the output is an exponential blend of the current observation and the prior output, using the coefficient and one minus the coefficient as the two weights. Until N plus one bars are available, the output is set equal to the current observation rather than the recursive update.