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Fourier Transform
Description
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. MetaStock Pro removes these
discontinuities by passing the data through a smoothing function
called a "hamming window."
Interpretation
It is beyond the scope of this website to provide complete
interpretation of FFT analysis*. The remainder of this section
explains the interpretation of MetaStock Pro'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.
* 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).
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