Building the relative-strength-index from signed close changes

Assemble a momentum measure from signed closes

The relative-strength-index is assembled as a momentum measure from the net close-to-close change, split into advancing sessions and declining sessions.

The columns to keep in view are the signed-change series, the averages built from them, RS, and the final 0-100 reading.

Store up-session and down-session changes

An advancing session stores the positive close-to-close change; a non-advancing session stores zero. That stored value is the up-session-change.

A declining session stores the absolute close-to-close drop; a non-declining session stores zero. That stored value is the down-session-change.

Place the seed-average on the completed lookback row

The first 14-period averages of the up-session and down-session series are simple means placed only on the completed seed row.

Each seed-average is computed once over the full lookback before recursion starts.

Continue with the recursive-smooth

After that seed row, each new average equals 13 times the prior average plus the newest session value, all divided by 14.

That update is the recursive-smooth: it weights the prior average by 13, adds the newest signed change, and divides by 14.

Form RS and apply the bounded-transform

RS is the up-session average divided by the down-session average, and the worksheet then adds 1 to that ratio.

The final step is 100 minus 100 divided by that one-plus-RS quantity, which confines the oscillator to a 0-100 range. That map is the bounded-transform.

Inspect the completed worksheet

A completed 14-period worksheet is shown for an example listed equity series so the full column layout can be checked.