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."
510
days Cycle seems Powerful in CMC stock:
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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