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<BLOCKQUOTE
>
----- Original Message -----
<DIV
>From:
Dave Merrill
To: <A title=amibroker@xxxxxxxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Friday, May 14, 2004 11:00 AM
Subject: RE: [amibroker] Re: DTFFT
<SPAN
class=018055914-14052004>Has anyone done anything MESA-like in AFL? Does
anyone know anything about MESA's internals beyond this?
<SPAN
class=018055914-14052004>
<SPAN
class=018055914-14052004> <A
href="">http://www.mesasoftware.com/#How%20MESA%20Works
<SPAN
class=018055914-14052004><FONT face="Courier New" color=#0000ff
size=2>
Here is
where you start:
<SPAN
class=018055914-14052004>
<FONT color=#008080
size=2>"The mathematical engine in MESA98 is the Burg algorithm. (Phd. Thesis
by John Parker Burg, Stanford University, 1975) This algorithm has been
successfully used in the MESA program since 1978. The mathematical procedure
is rather complicated and MESA98 compromises some generality to achieve ease
of operation. For example, the order of the mathematical filter is fixed
relative to the data length. MESA98 models the market as a generalized filter.
This filter is driven by a white noise generator. (White noise consists of all
frequencies with a uniform power amplitude.) The output of the filter is
compared with the samples of actual market price data. The result of the
comparison is fed back to adjust the filter so that, ultimately, the filter
output is a good replica of the true data in the time domain, within the
constraints of the filter. The length of data used to tune the filter can be
selected independently from the filter characteristics. MESA98 features an
adaptive data length. In general terms, a fraction of yesterday's dominant
cycle is today's data length. The adaptive data length avoids measurement
latency, or lag, usually produced by a fixed length data window. For example,
if a new 10 day cycle appears, we don't have to wait for it to fill a 30 day
window before we sense it in the measurement. A secondary measure of the price
data has been established within MESA98 when the filter is tuned. The
frequency information described by the filter settings. Since the filter
parameters were fixed by the price data, the digital clock can be run into the
future so that the filter output is a predictor of future prices where the
cycles retain their characteristics."
<SPAN
class=018055914-14052004>
<SPAN
class=018055914-14052004>Dave
<SPAN
class=018055914-14052004>
<BLOCKQUOTE dir=ltr
>
FWIW, the following blurb from Ehlers website
raises some concerns about FFT. Charts regarding FFT are
on:
<A
href="">http://www.mesasoftware.com/#FFT%20Comparison
Bill
<FONT
color=#0000ff>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. MESA2002 accurately extracts
short term cycles using an adaptive short data length, and therefore
MESA2002 should be your cycle measurement method.
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