TRIX: Triple Exponential Smoothing Oscillator
by Jack K. Hutson
Relating the use of Fourier spectrum analysis to stock or commodity data filter selection has been the
subject of a number of articles in Technical Analysis. In particular, Warren uses Fourier, in "Optimizing
TRIX: Further Analysis of Triple Exponential Smoothing" (September 1983 Technical Analysis), to
select TRIX's filter coefficients. The problem with any exponential moving average type filter is to
properly choose "alpha", the filtering constant. Warren's article was important because he was able to
mathematically manipulate our TRIX algorithm to obtain its transfer function. The transfer function is an
important tool in the design of filters and may be used to precisely relate cycle frequency and filter
coefficients, such as "alpha" in TRIX.
TRIX is obtained by triple exponentially smoothing the logarithm of daily market closes, then taking a
one day difference (momentum). In TRIX the "alpha" used for each pass through (three times) the
exponential filter process is the same, thus simplifying optimization. Warren used a frequency spectrum
generated by Fourier analysis of daily market closes to choose a cutoff frequency. This is an excellent
example of using a frequency spectrum of past data to estimate the significance of price moves. We
should be able to pinpoint where the power in a spectrum drops off and therefore where shorter cycles are
not useful for trading daily price swings. This point is called the high frequency cutoff frequency. Warren
explained how to convert cutoff frequency to TRIX "alpha" by the use of a chart in the above-mentioned
article. The following change to my original TRIX (July 1983 Technical Analysis) BASIC computer
subroutine eliminates the need of a chart. All that is required is the cutoff frequency in cycles per year.
TRIX will then filter out all cycles that are less than the cutoff frequency.