Constructing lag-reduced double exponential averages for MACD

The lag that comes with a longer average

A moving average is a windowed smoother that damps short-term fluctuation in an ordered price series while adding delay that grows with window length. Lengthening the average reduces noise but also increases lag, the delay between a change in the underlying series and the matching movement in the smoother.

Equal weights when the series is locally constant

A simple moving average assigns equal weight 1/w to each observation in a window of length w. It is described as most appropriate when the series can be treated as locally constant.

A recursive exponential average

Exponential smoothing is a recursive weighted average that mixes the newest observation with the previous smooth through a smoothing-constant between zero and one.

A single exponential moving average is computed as the current close times alpha plus the previous average times one minus alpha, with the smoothing-constant alpha equal to 2/(w+1). For a 26-period window that constant is 0.074.

Exponential smoothing is presented as a descriptive forecasting device rather than a procedure grounded in formal inferential statistical theory.

When a linear trend is present

When a linear trend is present and its intercept and slope change across successive windows, equal-weight averaging is treated as inadequate and double exponential smoothing is introduced. A modified one-parameter double exponential smoother is constructed to produce less lag than a single exponential moving average while still smoothing the series.

A faster composite labeled DEMA1

The faster average labeled DEMA1 is defined as twice the single exponential smooth minus the double exponential smooth of that first smooth. DEMA1 is a composite smoother, and it is distinguished from using the double smooth by itself.

The same MACD lengths on either filter

MACD is an oscillator formed from the gap between a shorter and a longer smoother, with a third smoother of that gap used as a trigger. It is constructed as the difference between a 12-period and a 26-period smoother, with a 9-period smoother of that difference used as the trigger. The same three lengths can be filled with either single exponential averages or DEMA1 filters.

Because the double-smoothed construction responds more quickly, lookback lengths may need to be increased so that random fluctuations do not dominate the indicator.