Phase diagrams for moving-average trend filters

What phase measures

For a simple moving average, phase is the signed distance of the close from that average. The reading is positive when price is above the average and negative when price is below it.

A phase-transition is defined as the indicator crossing the center of its range. For this trend-filter, that is the moment price crosses the chosen lookback.

How the diagram is drawn

An indicator-phase-diagram places lookback length on the horizontal axis and the signed price-to-average gap on the vertical axis. One snapshot then shows which lengths are currently above or below the filter.

Logarithmic horizontal scaling was used so a single diagram can compress lookbacks from very short to very long sampling intervals.

A single index snapshot

In the 1991-12-02 index snapshot, the close sat above lookbacks 5 through 12 and below lookbacks 14 through 70, locating the zero crossing at the 13-day average.

Why short lengths lead

Viewed as a sequence, transitions travel from shorter lookbacks toward longer ones because longer moving averages lag more and reverse later. That delayed march is the lookback-wave: the same crossing arriving later at longer sampling intervals.

When a crossing counts

Any single crossing was not treated as sufficient. Significance required the lookback to sit inside a broad, stable historical scoring band rather than a narrow isolated island.

On the index scoring map, isolated lookbacks below 43 were treated as unstable optimization-cliff islands. The contiguous 48-to-65 band was treated as the scoring-plateau, the region where a crossing would be taken as meaningful.

A listed-stock decision

In the listed-stock case, a 13-day crossing was rejected because it sat in a historically poor-scoring region. A later 38-day crossing inside a broad scoring-plateau was accepted as the state change.

Other ways to measure phase

Phase can be built as a raw price-minus-indicator gap, a percentage of the indicator, a standardized distance around an envelope, or, for bounded oscillators, a distance from the midpoint of the oscillator range.