Constructing an efficiency ratio adaptive average and entry filter

Seeding and the recursive update

After a lookback warmup, the adaptive average is updated recursively as the prior adaptive value plus a variable adaptive smoothing factor times the gap between the latest close and that prior value.

Until the bar count exceeds the lookback, the adaptive average is seeded to the current price instead of applying the recursive update.

Efficiency ratio and the adaptive smoothing factor

The efficiency ratio that drives the adaptive smoothing factor is the absolute net change over the lookback divided by the sum of absolute one-bar changes over the same lookback.

The adaptive smoothing factor is the square of a blend between a fast weight of 0.6667, equivalently 2/(2+1), and a slow weight of 0.0645, equivalently 2/(30+1), with the efficiency ratio as the blend weight.

When net change is large relative to path variation, the variable weight approaches its maximum and the average tracks price more closely. When prices zigzag, the weight approaches its minimum and the average flattens.

Increment filter and running extremes

Worked constructions use a lookback of 10 and set the companion increment filter to that lookback's standard deviation of successive adaptive-average changes multiplied by 0.15. The increment filter is a percentage of the lookback standard deviation of successive adaptive-average changes, used as a minimum travel distance.

A running low of the adaptive average is refreshed on down moves and a running high on up moves. Those running extremes are the reference points for the filter comparison.

Rule-based entry after a full band of travel

A buy condition is recorded when the adaptive average stands more than one increment filter above its running low. A sell condition is recorded when it stands more than one increment filter below its running high.

One coded system waits until the distance from the running extreme crosses above the increment filter and then acts on the close of that bar. That rule-based entry is a long or short condition that becomes true only when travel from the running extreme exceeds or crosses the increment filter.