Range-weighted construction of an adaptive exponential moving average

What the adaptive average is

The adaptive exponential moving average, or AEMA, is an exponential smoother that also measures where the current close sits inside the lookback high-low range. Its update uses a length-based weight and a second weight that rises when the close is near the lookback high or low and falls when the close is mid-range.

How construction proceeds

Construction starts with a simple moving average seed, then applies a length-based weight and a separate range-location weight before the recursive update. The recursive update is the prior adaptive value plus the length-based weight times one plus the range-location weight, times the gap between current price and the prior adaptive value.

Length-based and range-location weights

The length-based exponential weight, MLTP1, equals two divided by one plus the chosen number of periods. The range-location weight, MLTP2, is the absolute difference between the close-to-low and high-to-close distances, divided by the lookback high-low span, so the value sits between zero and one.

MLTP2 equals zero when the close is mid-range, is near one when price is at the lookback extreme, and is described as about 0.8 to 1 when price is near the period high or low.

Lookback period and initialization

The lookback period is the window that supplies the lowest low and highest high for the range-location weight. The lookback used for the high-low span can match the smoother length, but other windows can be substituted.

Initialization seeds both the exponential moving average and the adaptive average with a simple moving average of the chosen length before recursive updates begin. A worked ten-period example on the Russell 2000 seeds both averages with a ten-day simple average. A short history understates the recursive values, and a lookback of at least 250 periods is given as a way to raise accuracy.

Same-length and dual-length pairings

A same-length pairing plots an AEMA with an exponential moving average of identical length so their relative position can mark an overall trend. A dual-length pairing uses two AEMAs of different lengths to mark turning points and to generate crossover hypotheses.

A same-length adaptive and exponential pair is presented for trend location. Adaptive averages of different lengths are presented for turning points, filters, and double-crossover timing.

Double crossover on the chart

A double crossover is a paired-average event in which a shorter smoother crosses a longer one, used here as a trend or timing hypothesis rather than a standalone rule. Chart examples treat a short and long adaptive pair crossing while the long average is rising or falling as a way to describe a longer-term uptrend or downtrend.

Where the smoother loses usefulness

The construction is framed as a trend-following smoother that can lose usefulness in ranges. Crossovers are prone to whipsaws and are intended to be checked against other technical evidence.