Constructing TRIX from a cutoff to one shared alpha

What TRIX is

TRIX is an oscillator formed by triple exponential smoothing of log prices followed by a one-step difference. The archive builds it by applying the same exponential smoothing three times to the logarithm of daily closes and then taking a one-day difference of the thrice-smoothed series.

The finished oscillator is also described as a smoothed one-day momentum. The construction uses one shared alpha on all three exponential passes so that coefficient selection is reduced to a single constant.

Choose the shortest cycle that should remain

A frequency-spectrum plot of past daily closes is used to locate a high-frequency cutoff. At least 64 past daily observations are described as the practical minimum for that plot.

In the worked spectrum example, a 36.6-day cycle from 512/14 is treated as a starting cutoff, while a 27-day cycle from 512/19 is treated as shorter and filtered out. Cutoff frequency in cycles per year is computed as 130P/(N M). With P = 14, N = 512 and M = 1, the worked value is 3.55.

For daily data the usual cutoff band is given as 1.00 to 10.0 cycles per year, corresponding to removing cycles of 130 days or shorter versus 13 days or shorter. Cutoff frequency is the cycles-per-year threshold that marks which shorter oscillations the filter is meant to remove.

Turn that cutoff into one alpha

The computational routine accepts a raw alpha, a filter length converted as K = 2/(N + 1), or a cutoff frequency converted by C = (1 - cos(N * 0.024166)) / 0.25992 and K = C * (square root of (1 + 2/C) - 1).

Filter length is a lookback-in-days input that is converted into alpha instead of being used as a separate average. Editorial note: that length conversion is only another way to obtain the same shared alpha.

Reuse the same pass three times, then read the difference

Triple exponential smoothing is three successive exponential-average stages that share one alpha. The routine seeds the three recursive states with the logarithm of the first nonzero observation in the chosen input column.

Only after those three passes does the one-day difference turn the thrice-smoothed series into an oscillator reading. The routine stores a one-step change of the third smoothed value scaled by 10000 as the study output.

Judge lag with a moving-average baseline

Relative to a simple linearly weighted moving average, the exponential smoother is presented as having a comparatively short lag. That moving-average baseline is used only to judge how much lag the exponential construction is meant to reduce.