Filter stacks that combine a moving average with exponential smoothing

Two roles in one stack

A moving average is a lookback mean of ordered observations that updates once each sampling interval and is complete only after that interval closes. Exponential smoothing is a recursively weighted average that places more weight on recent observations and whose lag depends on length and restacking. Filter lag is the delay, in sampling intervals, between a change in the input series and the corresponding change in the smoothed output.

Estimate the unfinished average

A completed moving-average value is available only after the sampling interval closes, so an order staged before the next session cannot sit on the exact finished average. For a simple moving average, the observation that will leave the lookback is already known, which lets the next completed average be approximated before the interval ends. One approximation of the next-interval average uses the recent path of changes in the average itself rather than waiting for a precise close.

Feed the stack a composite observation

When the high and the low move in the same direction, a composite observation can be the average of those two prices. When they move in opposite directions, the composite can be the close. That composite series can then be passed through a short-period exponential moving average or a short end-point moving average. An end-point moving average is a short lookback smoother used here as the lower-lag counterpart to a short exponential average. An equal mix of the two is described as a compromise between amplitude smoothing and time lag.

Mix and restack to set filter lag

A generalized double exponential smoother can be written as a weighted mix of a single exponential moving average and a double exponential moving average. The mix weight controls how much lag remains. The lag of that mix is treated as a weighted average of the component lags, and applying the mix to its own output multiplies the estimated lag by the number of applications. With a five-period length and a mix weight of 0.7, three stacked applications produce an estimated lag of 1.8 sampling intervals.

Drop a restatement

Two daily indicator series that are highly correlated are treated as redundant. That indicator redundancy implies they describe the same aspect of price action rather than independent information. A combination is more informative when the pieces measure different aspects such as trend, momentum, and volume, or when the same smoother is applied on more than one time frame.