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Hello,
Paul, by this link http://web.gfi.uib.no/~ngbnk/kurs/notes/node122.html
i was poitning to the fact than :
1- From Signal Y(t), we compute Autocorrelation Corr(t).
2- From the FFT from the Autocorr you got the DSP.
(1) is included in the AR cose i posted (2 possibility: biased and not
biased).
(2) is included in the beta version of AB
So for now we can have DSP (= averaging FFT, considering it infinite with
finite component).
But i was pointing to the fact that, we can skip (2) and maximise spectral
representation by make some "estimation on the signal" or "use MEM".
So MEM (Maximum Entropy Method) leads mathematicaly to AR Spectral Method.
It is exactly same thing.
AR Spectral Method is a parametric spectral estimation method. You compute
an AR Model in time dimension, and after dirrectly from the coefficients and
from the variance of the innovation (error), you got the DSP (Density
Spectral Power), wich is same than Correlograme or Average Periodogramme.
The fact is there is not need of FFT or DFT : ))) and the noise is
filtered...
and this extract pretty well exctract resonancy from the spectrum.
AR (Auto Regressive) is good for signal presenting some main resonant
frequency.
On the oser side, you have MA (Moving Average), wich is good for inverse
(big lack of some frequency).
A long AR model can model a MA model.
ARMA (Auto Regressive Moving Average) model (combine both aspect and can
make great spectral estimation of more large variety of signal... ARMA = AR
+ MA)...
I am trying woking on ARMA, but very difficult to assume
stable/robust/convergent filter... need to compute some criterions and test
pole/zero to assume stability... to much work...
I think i will just use AR. With some pre-processing on the data (denoising
with classic MA used for trading) and choose a big number of coefficient for
AR Model, we converge to ARMA : )))
ARIMA is arma, but with trend/some seasonality consideration. Can be
computer by adding linear trend or polyfit.
ARIMA = preprocessing (classic MA, detrending) + AR long.
Should do the trick maybe ; ) ... to test.
SARIMA, ARMAX, ARX, ARCH, GARCH, are all some different version of AR
modeling i thing (i don't know very well ARH, GARCH, seems good to estimate
volatility for trading options).
I just finish this technic post by a link :
http://irevues.inist.fr/bitstream/2042/3241/1/004.PDF+TEXTE.pdf
it's in french, sorry... but just look at page 40.
It show difference with AR Spectral Parmaetric Method (i.e: MEM) and classic
FFT for finding sinus in noised data. Pretty good isn't it ?
Finished, hope i didn't bother you too much... this was just to give some
idea to work on for futur indicator based on cycle determination and which
go further than classic FFT wich make zero assumption about signal spectrum
pattern (AR make assumption that resonant frequency are present in signal).
If I manage to make good sinus extraction from AR Spectrum Estimation, I
will post some code.
But stock quotes data spectrum seems more to refer to AR model than MA i
thing, so this presumption on the data can bring us more clean cycle
determination.
Maybe we need in Amibroker in some near future special plot window for
frequency domain in real time... who knows : )
Cheers,
Mich.
----- Original Message -----
From: Paul Ho
To: amibroker@xxxxxxxxxxxxxxx
Sent: Sunday, November 12, 2006 6:15 AM
Subject: RE: [amibroker] Re: Polynomial Trendlines
Mich,
So maybe someone can help me : is it possible to compute a DSP from
AR coefficient based on the formula for AR i post (there is code to
compute biased or not biased autocorrelation function inside). Do
someone try ?
What link are you referring to,
http://web.gfi.uib.no/~ngbnk/kurs/notes/node122.html, there is no code with
this link.
Anyway, the power spectrum function is given in a number of references
including the one that i posted. I am still currently working on mine but is
not complete.
Cheers
Paul.
From: amibroker@xxxxxxxxxxxxxxx [mailto:amibroker@xxxxxxxxxxxxxxx] On Behalf
Of tomy_frenchy
Sent: Sunday, 12 November 2006 12:14 PM
To: amibroker@xxxxxxxxxxxxxxx
Subject: [amibroker] Re: Polynomial Trendlines
MESA, MEM seems to use the DSP (Density Spectrum Power) of the
autocorrelation function.
Seem it is corresponding in some sort to AR modeling.
http://web.gfi.uib.no/~ngbnk/kurs/notes/node122.html
It is mentionned to the link you gave too :
http://www.library.cornell.edu/nr/bookcpdf/c13-7.pdf
AR = MEM ...
So maybe someone can help me : is it possible to compute a DSP from
AR coefficient based on the formula for AR i post (there is code to
compute biased or not biased autocorrelation function inside). Do
someone try ?
Does it exhibit more clearly cycles ?
Seems there is some interresting link between AR and MEM to be
exploited maybe ?
Thanks,
Mich.
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