Evaluating an adaptive moving average against a same-window moving average

Delay versus residual noise

A long simple moving average can suppress noise while imposing a delay equal to half its lookback, illustrated by a 200-day window that waits 100 days for an answer. A short simple moving average answers quickly but leaves more residual noise, illustrated by an 11-day window whose delay is only five days.

Editorial interpretation: those two windows show the first two sides of the trade-off. Add spike distortion as the third, then judge an adaptive moving average against a same-window moving average on all three rather than by a single overlay.

How jagged the input already is

Among tested open-high-low-close combinations, the open-close midpoint had the fewest turning points at 38.84 percent and the lowest average neighbor divergence at 0.50 percent. Closing price alone was the roughest tested input, with about 49.05 percent turning points and 0.94 percent average neighbor divergence.

When a spike enters and leaves the window

A simple moving average can reverse twice around one spike, once when the jump enters the window and again when it leaves. When a 2.00 up move enters a 10-day simple window as a 7.00 up move exits, the average can fall by 0.50 instead of rising.

Adaptive moving average versus the same window

A same-length adaptive average can stay flatter through a rally than an exponential average while turning later, as in a 15-day overlay on Malaysia iShares from 21 May to 31 August 2012. On the reported comparison, the adaptive average had about 20 percent more delay than a simple moving average with the same averaging period.

Editorial interpretation: extra flatness is not a free gain if the adaptive moving average turns later. Keep the same averaging period on the moving-average baseline and score both lines on residual noise, phase delay, and how they handle a spike.