Constructing the true strength index with double exponential smoothing

The finished reading

The true strength index is one hundred times the ratio of double-smoothed one-period close change to double-smoothed absolute one-period close change.

One-period momentum is the signed close-to-close change that enters the numerator path before any smoothing. Absolute momentum is the unsigned size of that same one-period close change and is reserved for the denominator path.

The index itself is the twice-smoothed signed series divided by the twice-smoothed absolute series and then scaled by 100.

Inputs for each path

Signed momentum is the one-session difference between successive closing prices. That signed difference is one-period momentum. Absolute one-session close change is absolute momentum.

Both the signed change and its absolute value are passed through an inner exponential average of length r and then an outer exponential average of length s.

How the nested updates are written

The inner exponential average is the first recursive smoother, labeled with lookback r, and is applied independently to signed and absolute momentum. The outer exponential average is the second recursive smoother, labeled with lookback s, and is applied to each already-smoothed series.

The worked construction uses an inner length of 40 and an outer length of 20. The first exponential update of signed momentum uses a smoothing constant of 0.049 on the gap between the latest momentum and the prior smoothed value. The second exponential update of the already-smoothed signed series uses a smoothing constant of 0.095 in the same recursive form.

A smoothing constant is the blend weight that updates an exponential average from its prior value toward the newest observation. Absolute one-session close change is updated with the same two-stage constants of 0.049 and then 0.095.