Constructing a volume and move-adjusted trend filter

What a moving average records

An average of ordered closes, with any lookback or any linear or exponential decay of those closes, only locates the history of the series. It does not, by itself, state a future direction. Without extra inputs, that moving average only describes the path already observed over a chosen lookback.

The lookback is the fixed count of bars whose closes, absolute changes, and volumes later enter the two weight vectors. Until those extra series are written in, the average remains a record of history, not a statement of future direction.

How move size and volume enter the weights

A directional reading from an average is treated as possible only after an extra series that can lead price, such as move size or volume, is written into the weights.

The move-adjusted average divides each bar’s absolute close-to-close change by the sum of those absolute changes over the lookback, counting the change into the first lookback close from the prior close outside the window, then sums the closes times those shares.

A separate volume-adjusted average divides each bar’s volume by the sum of volume in the same lookback and sums the closes times those shares. Volume-price analysis, in this construction, uses the volume that accompanies each close-to-close change to raise or lower that bar’s share of the average.

The combined-volume-move-average is the arithmetic mean of the move-adjusted average and the volume-adjusted average. After move size and volume have been written into the weights, that constructed line is the trend filter used to separate directional persistence from noise.

Equal move weights and constructed paths

When successive absolute price changes are identical, the move weights are equal, so the move-adjusted average coincides with a simple average and only the volume weights can change timing or shape.

On a constructed path where volume bottoms at price peaks and troughs and tops as price crosses the midpoint, the combined line turns after a trough and after a peak sooner than the move-only line and tracks a smoother path than either the move-only line or a simple average.

On a constructed path where volume extrema coincide with price extrema, the combined line has larger amplitude than the move-only line and changes more promptly than the move-only line or a simple average.

How volume raises or lowers a bar’s share

A large same-direction change on heavy volume receives more weight than a large change on light volume. A light-volume thrust that then reverses on heavy volume is reduced in the combined average.

Fading volume into a range extreme is presented as consistent with remaining inside the range, while rising volume into an extreme is presented as a reason the combined line should respond faster if the move continues or the range breaks.