Constructing a bounded correlation-trend-filter

Assembling the filter

A trend filter can be assembled by correlating an ordered price series with a straight reference line that has a positive slope. In this construction the correlation-trend-filter is that lookback correlation between observed prices and an explicit upward linear reference, used as a bounded reading of directional regime.

The linear-slope-reference is a synthetic straight line with a fixed positive slope that stands in for an idealized trend path over the estimation window.

Over the chosen lookback, a rising price path produces a correlation near +1, a falling path produces a correlation near -1, and a sideways or oscillating path produces little correlation. The construction confines the output to the closed interval from -1 to +1, so the same filter can be applied to different symbols without rescaling.

Choosing correlation-length

Correlation-length is the number of bars in the window. It sets both the intended holding-period scale and the expected delay of the reading. The reading lags by about half the correlation-length, so a 10-bar window can mark onset or failure with less delay while a 40-bar window is smoother but later.

Correlation-length can be sized to an intended holding interval: a 20-bar window for a hold of about one month, and a 40- to 60-bar window for a hold on the order of a quarter year.

A shorter correlation period can be used first to mark trend-onset-and-failure, then lengthened as a directional move persists. Trend-onset-and-failure is the movement of the bounded reading away from or back toward zero, used to mark when a directional regime starts or ends.

Cyclic-mode-reading

If the correlation-length is shortened to about half a cycle, the same measure can follow the cyclic component. That cyclic-mode-reading turns positive on the upswing and negative on the downswing, with lag of at least a quarter cycle when the length is half the cycle.

Worked implementation

A worked implementation correlates closing prices with a linear time index that is signed so the reference slope stays positive when the window is counted backward. It then applies the standard two-variable correlation ratio after confirming that both series have nonzero variance.

The product-moment-guard is that zero-variance check on both series before forming the two-variable correlation ratio, so the filter is undefined rather than unstable when a window has no spread.