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Fourier
Transform
Description
It
is beyond the scope of this website 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.
MetaStock
Pro 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 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. |
