Smoothed relative-strength construction from wilder-averaging and a price prefilter

How the oscillator is assembled

The relative-strength-index is a bounded oscillator assembled from averaged up-moves versus averaged down-moves over a stated lookback. Exponential-smoothing is a recursive average that replaces a fraction of the prior average with a fraction of the newest observation.

The original relative-strength construction uses a simple average only to seed the first window, then updates with a 1/n recursive blend rather than a 2/(n+1) exponential factor. That wilder-averaging convention keeps a 1/n blending factor and a simple-average start, and it is distinct from the 2/(n+1) exponential convention.

An equivalent ratio-form

A ratio of net change to total absolute change, each recursively averaged, is an algebraically equivalent rewrite of the original relative-strength formula once the same averaging convention is used. That ratio-form is a scaled net-change average divided by a total-change average.

Initialization and the settling span

Initialization is the first-window calculation that seeds a recursive average, often a simple mean of the opening observations. If the recursive average is started without the simple-average seed, agreement with the original construction appears only after a settling span of about two or three times the lookback.

The lookback is the sample length that sets both the average span and the time needed for a recursive average to settle.

A triangular-prefilter on the close

A six-bar triangular smoother of the close can be formed as a double simple average and supplied as the price input to a subsequent relative-strength calculation. That triangular-prefilter is a short finite-impulse-response smoother applied to price before oscillator inputs are formed.

One platform pairing applies that six-bar triangular-prefilter to the close and then computes relative strength on a 10-bar length.

Competing prefilter and change pairings

A competing construction first applies a four-weight close smoother, then totals signed changes over a 10-bar window instead of recursively averaging those changes. That summation-form totals raw up and down changes over the lookback rather than recursively averaging them.

The same four-weight prefilter can be paired with the original recursive averaging of up and down changes and then mapped through the classic 100 minus 100 over one-plus-ratio transform.

Spreadsheet accumulation

A spreadsheet implementation of the prefiltered oscillator accumulates up and down increments of the smoothed close over the chosen length and returns their share of the combined total when that total is nonzero.