Constructing a multi-horizon folded-correlation reversal filter

Folded correlation as the event

Folded correlation treats a reversal as the bar where pre-turn and post-turn segments match after one segment is reflected. Folding an idealized V-shaped price path about its trough or peak makes the two equal-length segments highly correlated. The same fold placed mid-trend does not.

The lookback horizon carries a delay

The lookback horizon is the paired sample length whose midpoint is the folding location. When the two segments have equal duration, the strongest correlation is delayed by half the lookback: a 13-bar window places that reading 7 bars later, and a 39-bar window places it 19 bars later.

A brief interruption still scores as a high-correlation event only if the lookback is no longer than twice the interruption span. A longer window mixes in uncorrelated prices and lowers the score. A short lookback produces more numerous, more current correlation spikes. A long lookback suppresses those interruptions and reports older turning points.

Smooth before the fold

The computational sequence is to apply a super-smoothing filter, correlate one half of the lookback with the negated other half, then rescale the resulting autocorrelation from -1 to +1 onto 0 to 1. Exponential smoothing is that low-lag smoother. It is applied to raw prices before folding so that short interruptions are damped and do not register as extra correlation spikes.

An autocorrelation test at every horizon

The autocorrelation test compares one half of a lookback window with the negated other half after the series is folded at a candidate turning point. Each horizon keeps its own delay, because the strongest reading still arrives half a lookback after the fold.

A trend filter only signs the peak

After the autocorrelation peak, the slope of the smoothed series immediately beforehand is used as a trend filter. That signing rule labels the event as a top or a bottom. It reads the already-smoothed series just before peak correlation and does not create the event.

A heatmap of lookback against time

Plotting correlation as color against a vertical lookback axis yields a time-aligned heatmap in which major reversals appear as long backward-pointing features and interruptions as shortened remnants. Because the shortest window still needs a finite sample, the heatmap can be shifted four bars toward the turning point, in the same spirit as a centered moving average.