Constructing the commodity channel, average directional, and relative strength indexes on a shared cycle scale

A shared construction pipeline

Editorial reading: TradersWeek treats the commodity channel index, the average directional index, and the relative strength index as one construction pipeline with interchangeable inputs.

The shared stages are: choose a price increment, average it over a cycle-linked window, form a guarded ratio, then smooth and map the result onto a shared scale.

The teaching aim, also editorial, is to rebuild each stage so the three models differ by what they feed the pipeline, not by unexplained formulas.

What the work matrix holds

A work matrix stores temporary columns before the final ratio is formed.

Those columns hold typical prices for the commodity channel index, directional increments for the average directional index, or close-to-close changes for the relative strength index.

Commodity channel index

The commodity channel index is a cycle-window residual of typical price, divided by the mean absolute deviation of that residual and then scaled for display.

Commodity-channel construction first replaces each bar with typical price, the mean of its high, low, and close, then replaces that series with a moving average whose length is the dominant cycle.

That full-cycle window is the dominant-cycle lookback. It averages typical price and the absolute deviations of the residual.

The commodity-channel residual is divided by that dominant-cycle average of absolute deviations, scaled so the interval from minus two to plus two occupies the vertical band from 140 to 190, and clipped at those band edges.

Display clipping forces the unbounded ratio to stay inside the fixed vertical band so extreme readings do not leave the plot.

Average directional index

Here the average directional index is built as a directional-trend oscillator: successive high and low increments are separated, averaged, and turned into a signed, guarded ratio.

Average-directional construction compares the change in successive highs with the change in successive lows, keeps only the larger increment, and writes zeros to both sides when neither extreme expands.

The plus and minus directional increment series are each averaged over a quarter-dominant-cycle window before any ratio is formed. That shorter window is one fourth of the dominant cycle.

If both directional averages are zero, the routine writes the midpoint display value 165 instead of computing a ratio. Otherwise the signed ratio of their difference to their sum is mapped into the 140-to-190 band and averaged again over the quarter-dominant cycle.

Relative strength index

The relative strength index is a twice-smoothed ratio of averaged up closes to the sum of averaged up and down closes.

Relative-strength construction records successive close-to-close changes and accumulates the up moves and the down moves as two separate quarter-dominant-cycle averages.

When both relative-strength component averages are zero, the interim ratio is set to one half. Otherwise it is the up average divided by the sum of the two averages.

A second quarter-cycle average is then mapped from the unit interval onto the shared 140-to-190 band.

One display band and two lookbacks

All three oscillators share one vertical display region from 140 to 190 with interior guide lines.

They differ in the lookback the operator supplies: a full dominant-cycle length for the commodity channel index versus a shorter cycle or day count for the directional-trend and relative-strength routines.