Cycle-aligned directional trend indicator

From an unsigned index to a signed indicator

Classic directional movement averages daily up and down high-low differences twice over a 14-day span, treated as a typical half-cycle. It then forms an unsigned index as the absolute MU minus MD gap divided by their sum, and averages that index again to obtain Average Directional Index.

This construction replaces the unsigned index with a signed interim directional ratio, IN equals (MU minus MD) divided by (MU plus MD). That ratio is then averaged to obtain Directional Trend Indicator, a signed directional series built from averaged up and down high-low differences, then averaged again, so the finished oscillator is meant to crest and trough with price when a cycle is present.

Spending the phase lead

On a pure sine wave, a half-cycle moving average lags by about 90 degrees, while a full-cycle average is zero and recovers an underlying trendline. Differencing successive highs or successive lows leads a cyclic series by about 90 degrees. That phase lead from differencing, paired with averaging, is the mechanism used to restore phase alignment with price.

Averaging the up-move and down-move series over a quarter-cycle average, then averaging the interim directional ratio over another quarter-cycle average, is intended to give Directional Trend Indicator a net half-cycle lag and place it in phase with price. The dominant cycle is the prevailing periodic length used to size those averaging windows.

A two-stage average and a decision rule

The stated Directional Trend Indicator decision rule marks a downward hypothesis after a crest and an upward hypothesis after a valley, and only when the absolute value of the indicator exceeds 0.7.

Splitting one half-cycle average into two quarter-cycle stages is presented as a way to reduce sensitivity to a wrong cycle-length guess. On an 80-unit synthetic sine wave, turning marks stayed usable when the cycle input was 80, 40, or 120. The derivation treats that as tolerance to about a 50 percent cycle-length error.

A sine-like shape as the cleanliness check

On synthetic sawtooth and reduced-harmonic waveforms, a sine-like Directional Trend Indicator shape is treated as evidence that a usable dominant cycle is present and that turning marks remain well placed at cycle inputs of 80 and 120.

The construction is described as most reliable when other spectral components sit about 10 dB, or about one-third the amplitude, below the dominant cycle, or when Directional Trend Indicator itself looks like a sine wave. The dominant cycle is also the length used to judge whether other rhythms are weak enough for the construction to stay interpretable.

Average Directional Index in this construction

In this construction, Average Directional Index remains a second long average of unsigned directional movement. It collapses toward a late trendline of the indicator rather than marking turns in phase with price.