Constructing a slope-corrected moving average

Write the lag into the construction

A modified moving average is assembled from a simple average of a chosen price series over a stated lookback, then adjusted by a slope term. That slope correction lets the construction offset the lag that the unadjusted average of the same lookback typically introduces.

TradersWeek editorial: treat lag as a written term in the construction, a simple-average level plus an explicit slope correction, rather than a hidden property of the plotted line.

Form the slope sum

The slope term is formed by looping across the lookback and weighting each lagged price by one-half of the lookback minus an odd-numbered factor. That odd-numbered factor starts at 1 and increases by 2 at each older bar.

The resulting slope sum is a weighted accumulation of current and lagged prices that estimates local direction for the correction term. Lookback length is the number of sampling intervals used for both the simple average and the slope weights.

Finish the modified average

The finished value equals the simple average plus six times the slope sum, divided by the product of the lookback and one plus the lookback.

Call it from a plot routine

Wrapping the construction as a function of price and length lets a separate plot routine call it with defaults of the close and a two-bar lookback, scaled like the underlying series.

Check the short-lookback reductions

For a two-bar lookback the construction reduces to a two-bar simple average of the close plus one-half of a one-bar momentum. For a three-bar lookback it reduces to a three-bar simple average plus one-half of a two-bar momentum.

Those short-lookback reductions are algebraically collapsed forms of the same construction, in which the slope correction becomes a momentum term divided by two.

Use a loop when the lookback grows

Expanded forms for four-, eight-, and ten-bar lookbacks keep the same two-part structure: a simple average plus a linear combination of the current close and successively lagged closes, scaled by the product of the lookback and one plus the lookback.

When the lookback is longer than three bars, writing every lag weight by hand becomes cumbersome, so a looped or parameterized implementation is used instead of a fully expanded formula.

A four-bar worksheet form

A four-bar worksheet form computes the simple average, a four-term weighted sum of the current close and the prior three closes, applies the six-over-(period-plus-one)-times-period adjustment, and can store the residual of close minus that modified average.