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At 4:07 PM -0500 7/17/00, Clyde Lee wrote:
>Be extremely careful in using FFT's ! ! !
I would strongly concur with this statement.
Below is a quote from John Ehlers web site on the topic. He is
selling MESA software so has a vested interest but his explanation of
the problems with using Fourier analysis in trading is quite accurate.
Bob Fulks
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From: <http://www.mesasoftware.com/>
MESA COMPARED TO FOURIER TRANSFORMS:
FFT is the acronym for Fast Fourier Transform. FFT is a computer
algorithm to perform the Fourier Transforms rapidly. The correct use
of Fourier Transforms is subject to several constraints. First, the
data must be stationary (non-shifting) over the observation period.
Secondly, an integer number of cycles must be used in the analysis.
The Nyquist theory of sampled data systems states that there must be
at least two samples per cycle. These constraints pose a dilemma for
analysis of price data.
For example, if we have data consisting of 64 points (64 days in the
market), the longest cycle we can measure is 64 days. The next
longest cycle is 64/2=32 days. The next longest available cycle is
64/3=21.3 days. The next cycle is 64/4=16 days, etc. The 64 day data
simply does not provide good resolution to identify the cycles
because there is a 5 day gap between measured results right in the
most active cycle region. The only way to increase resolution is to
increase the data length. However, if the data length is increased
there is a significantly lower probability that the cycle has not
shifted over the entire data length. In fact, it is downright
unlikely.
Thus the use of FFTs for trading is not advisable. MESA2000
accurately extracts short term cycles using an adaptive short data
length, and therefore MESA2000 should be your cycle measurement
method.
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