Fourier Transformation Cycles 

It is beyond the scope of the manual to provide a full explanation of Fourier analysis.  Further information can be found in Technical Analysis of Stocks & Commodities magazine (TASC), Volume One issues #2, #4,  and #7; Volume Two issue #4; Volume Three issues #2 and #7 (Understanding Cycles); Volume Four issue #6; Volume Five issues #3 (In Search of the Cause of Cycles) and #5 (Cycles and Chart Patterns); and Volume Six issue #11 (Cycles).

Fourier Transforms were originally developed as an engineering tool to study repetitious (cyclical) phenomena such as the vibration of a stringed musical instrument or an airplane wing during flight. 

The complete analysis concept is called spectral analysis.  Fast Fourier Transform (FFT) is an abbreviated calculation that computes in seconds rather than minutes.  The FFT sacrifices phase relationships and concentrates only on cycle length and amplitude (strength). 

The benefit of FFT is its ability to extract the predominate cycle(s) from a series of data (e.g., an indicator or a security's price). FFTs are based on the principal that any finite, time-ordered set of data can be approximated arbitrarily well by decomposing the data into a set of sine waves.  Each sine wave has a specific cycle length, amplitude, and phase relationship to the other sine waves. 

Problems occur when applying FFT analysis to security price data because FFTs were designed to be applied to non-trending, periodic data (whereas security price data tends to be trending).  This is overcome by "detrending" the data using either a linear regression trendline or a moving average.  

Security data is not truly periodic, since securities are not traded on weekends and some holidays.  A software removes these discontinuities by passing the data through a smoothing function called a "hamming window." 

Interpretation:-

       As stated at the beginning of this section, it is beyond the scope of the manual to provide complete interpretation of FFT analysis.  The remainder of this section explains the interpretation of MetaStock's Interpreted FFT. The Interpreted FFT displays an indicator that shows the three predominate cycle lengths and the relative strength (i.e., the relative amplitudes) of the cycles. The Interpreted FFT indicator is always displayed from the most significant cycle to the least significant cycle.  The longer the indicator remains at a specific cycle length, the more predominate it was in the data being analyzed. 

Once you know the predominate cycle length, you may want to use it as a parameter for other indicators.  For moving averages, use 1/2 of the cycle length for the optimum number of periods.  For example, if you know that a security has a 40-day cycle, you may want to plot a 20-day moving average. 

 

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