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----- Original Message -----
From: "DIMITRIS TSOKAKIS" <<A
href=""><FONT
size=2>TSOKAKIS@xxxxxxxxx<FONT
size=2>>
To: <<A
href=""><FONT
size=2>amibroker@xxxxxxxxxxxxxxx<FONT
size=2>>
Sent: Thursday, October 09, 2003 8:28
AM
Subject: [amibroker] Re: FW:
Optimize/OverOptimize
snip
> 2. I do not appreciate Ehlers analysis for one
basic reason : He is > quite deterministic.> I may call some
function sinusoidal, but if it is not sinusoidal, it > is a mistake to
speak about phase, shift etc. The attempt to > introduce in T/A complex
variables and analysis through some quasi-> polar coordinate system is
not sucessful, especially at the critical > points.
I have not looked into this in great
detail, but the following is a summary of what Ehlers has to say
regarding FFT vs. MESA. On the surface it appears to be something to
consider.
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.
COMPARISON OF FFT AND MESA
MEASUREMENTS
Measured spectra are usually plotted as amplitude versus cycle period as
shown in the figure below. The amplitude is often measured in decibels (db)
because this logarithmic scale can display a wider dynamic range. For example, a
20 db amplitude range is a power ratio of 100:1. The display usually appears as
a bell-shaped curve. The sharper the bell the more the energy is focused at a
single cycle period. A highly focused spectrum is a spike in the spectrum
display.
To enable plotting the spectral estimate in time synchronization with the
barcharts, we convert the amplitude of the spectrum to colors as shown in the
figure below. Using these colors, we can plot the spectrum continuously as a
contour plot below the barchart. A highly focused measurement would show as a
yellow line in this contour plot. A poorly focused or low resolution measurement
is a fat bell curve, and would show up as having the yellow color splattered
over a range of cycle periods.
<IMG height=166 src="gif00559.gif"
width=280>
The charts below compare the FFT measurements on the left to the
MESA measurements on the right. The first row is the comparison measurement of a
theoretical 24 bar sinewave. Clearly, the FFT measurement has poor resolution
while the MESA measurement is sharply focused at the theoretical period. The
second row is the comparison measurement of a real-world data sample. The FFT
yields essentially no useful information while the MESA measurement clearly
shows the changes in the cycle period.
<IMG height=378
src="" width=538>
snip
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