Inverting relative-strength-index closes for same-session rules

Construct the oscillator from close changes

The relative-strength-index is a bounded oscillator built from the relative-strength-ratio of the up-close-average to the down-close-average over a chosen lookback. Unchanged periods are counted as zero in both averages.

The oscillator is constructed as one hundred minus one hundred divided by one plus that ratio, with a conventional first window of fourteen periods.

Refresh the averages after the first reading

After the first reading, the two averages may be refreshed either by an exponential-update that blends each prior average with the newest change using a thirteen-of-fourteen weight, or by a simple-window-update that recomputes a simple fourteen-period mean of the signed close changes.

In the supplied fourteen-period close-change series the first up-close-average was 22.86, the first down-close-average was 14.29, the first relative-strength-ratio was 1.6, and the first oscillator reading rounded from 61.54 to 62.

A next-period up-change of 19 moved the exponential-update to about 63 and the simple-window-update to about 68, so the two updates diverge on the same increment. The exponential-update is described as smoother and slower to react. The simple-window-update does not depend on the length of the prior series and responds more quickly to new closes.

Set the lookback from a cycle

The conventional fourteen-period lookback is presented as a half-cycle-lookback of an observed average trading cycle near twenty-eight days, and a nine-period lookback as about half of a near-monthly cycle. When no cycle is identified both lengths can be run until one is retained for style consistency. Nearby lengths such as thirteen or fifteen are treated as nearly interchangeable with fourteen.

On a comparison of nine-period and fourteen-period readings, the indicator extremes differed in absolute level but lined up in timing and in how those extremes related to one another.

Solve a planned reading for a close

A planned next oscillator reading can be inverted into a required close-to-close change by combining the current up-close-average and down-close-average with the matching target-relative-strength from an oscillator-to-ratio translation table, using a residual count of lookback minus one, or the last lookback of raw changes if the simple-window-update is in use.

In the worked downside case a next reading of 71 or lower implied a target-relative-strength of 2.4483 or less. With prior averages 31.73 and 12.34 the required change was 8.06, so a drop of nine or more points would confirm.

When the next reading must rise, the complementary change is the residual times the down-close-average times the target-relative-strength, minus the residual times the up-close-average. In the worked case a target of 32 implied a target-relative-strength of 0.4706 and a required rise of 7.92, or eight points.

Bind the close as one same-session rule

That downside threshold can be placed as a close-only-stop, optionally widened to ten points to allow for closing-range variance. The close-only-stop can fill only if the session close reaches the precomputed distance from the prior close, so the loss or confirmation decision stays bounded until that close.

The same-session close can then complete one rule-based-entry for entry, exit, or abstention instead of waiting for the following session. Editorial reading: keep the inverted close and the close-only-stop together as a single testable procedure rather than as a next-day chart reading.