True strength index from signed, double-smoothed momentum

One-bar momentum needs averaging

One-bar momentum is defined as the current close minus an earlier close and therefore carries both the size and the sign of the price change.

Raw one-bar momentum of an unsmoothed close series tends to oscillate rapidly about zero, so some form of averaging is required before turning points are readable.

Smoothing reduces noise and adds delay

Averaging reduces jagged responses but also introduces delay, so very smooth moving averages can mark a turning point well after the corresponding price extreme.

Applying a moving average to momentum rather than to price is presented as generally producing less lag than averaging the price series itself.

How the Relative Strength Index is built

The Relative Strength Index separates one-bar momentum into up and down components, averages those components, and maps the ratio of the up average to the sum of both averages onto a 0-to-100 scale.

Because that construction still follows high-frequency price noise, the Relative Strength Index is described as better suited to amplitude and divergence readings than to clean turning-point calls.

A double-smoothed Relative Strength Index

A double-smoothed Relative Strength Index is obtained by applying two successive exponential moving averages, with constants 2/(y+1) and 2/(z+1), to the up and down one-bar momenta before forming the same ratio.

Those two passes apply exponential smoothing to the up and down one-bar momenta, not to the close series itself.

How the true strength index keeps the sign

The true strength index keeps signed one-bar momentum in the numerator and the absolute value of that momentum in the denominator, then double-smooths both series with exponential moving averages and multiplies the ratio by 100.

With only a single smoothing pass the true strength index differs from the Relative Strength Index by a scale factor. The second long-and-short smoothing pair is what distinguishes the construction and is presented as reducing choppiness while keeping lag acceptable.

A two-pass worked example

A worked true-strength-index example first applies a 14-period exponential moving average with constant 2/(14+1)=0.1333, then a 3-period exponential moving average with constant 2/(3+1)=0.50, to both signed momentum and absolute momentum.