Building momentum-scaled adaptive moving averages

A recursive average with a changing blend weight

An adaptive moving average is a recursive price smoother whose effective blend weight is allowed to change from bar to bar. A moving average in the same family is a recursive blend of the latest close with the prior average, using a fixed smoothing factor of the form two divided by a period plus one.

When the absolute momentum ratio is allowed to vary, the same exponential update that defines a fixed-length moving average becomes an adaptive average. A variable-length average can be built as a recursive blend of the current close and the prior average, with the blend weight equal to a fixed smoothing factor times that absolute momentum ratio.

Turn consecutive closes into a persistence reading

Each bar contributes its close-to-close change to only the up total or only the down total, not both. Signed-move sums are those separate running totals of upward closes and downward closes over a fixed window.

The momentum ratio equals the difference between a lookback sum of up-moves and a lookback sum of down-moves, divided by the total of those two sums. The absolute momentum ratio is the absolute value of that difference divided by the combined size of the two totals, and it is used as a zero-to-one scaler.

One complete parameterization uses a nine-bar window for the signed-move sums.

Scale the exponential update

The blend weight equals the fixed smoothing factor times the absolute momentum ratio. One complete parameterization uses a twelve-period input inside the exponential factor two divided by the period plus one.

The average remains a recursive blend of the current close and the prior average. The persistence reading changes only the weight inside that update.

Seed the recursion and withhold incomplete output

The recursion is seeded with the close after the signed-move window is available, then updated from its own prior value on later bars. That recursive seed is the first legal value of a self-referential series, commonly the close once the window is full.

A construction may withhold output until the adaptive value is positive so incomplete start-of-series readings are not plotted.

Add percentage envelopes last

Upper and lower envelopes can be drawn as one-percent multiples of the adaptive average rather than as independently smoothed series. A percentage envelope is the pair of upper and lower lines formed as constant fractional multiples of the adaptive average itself.

Envelope lines that depend on the recursive average also require their own recursive update steps.

A sibling lookback oscillator

The commodity channel index is a lookback price oscillator in the same quantitative-filter family. It is used here only as a sibling example of mapping a window of ordered prices into a scaled reading.