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Fred,
I had a look at Hurst's book - Appendix 6. The Grigonometric Function that
he is proposing, when reduced to its canonical form, is pretty much a
fourier series, isnt it? Rather than using Guassian Elimination - Least
Square Curve Fitting, Wouldn't be more direct to obtain amps, phase angles
and frequenies of the harmonics through FFT, and inverse transform to
recreate the trigonometric series? might have filter out some of the extreme
frequencies to get a nice curve. the order of the series can be determined
by minimising the square of the prediction error like that of Warren in his
MEM article.
Cheers
Paul.
_____
From: amibroker@xxxxxxxxxxxxxxx [mailto:amibroker@xxxxxxxxxxxxxxx] On Behalf
Of Fred
Sent: Saturday, 7 October 2006 12:48 AM
To: amibroker@xxxxxxxxxxxxxxx
Subject: [amibroker] Re: Polynomial Trendlines
TJ,
I have long since had FFT capability in AFL as the algorithms are
very straight forward and relatively simple to do in AFL. However
FFT's typically require LOTS of data relative to the cycle lengths
one is attempting to identify and do not provide particularly good
resolution at the lower frequencies. From this perspective tools
like MESA ( The algortihm, NOT the black box product ) provide much
greater resolution with much less data.
However, neither of these approaches is what I'm after at this
juncture ... What I'm after is the ability to do trigonometric curve
fitting in a similar way to what the PolyFit AFL I posted performs
linear curve fitting i.e. via the solution of simultaneous
equations. This involves some rather sophisticated ( at least from
my perspective ) math which can be found for example in Appendix 6
of J.M. Hurst's book. Since the discussion there is only about 3
pages I'd be happy to post it or email it to anyone who has an
interest and is so inclined if they'd like to read it and comment on
how to implement it.
Fred
PS ... Some final thoughts about FFT's and their implementation in
AB ... If you are going to provide this capability, please do so in
a manner that one can take advantage of ALL the information that
would be the product of performing an FFT i.e. both the real &
imaginary arrays or a single array of complex numbers and the
ability to deal with complex numbers in AFL. This is needed not
only to get amplitudes at particular frequencies but also phase
shift and power.
PPS ... IMHO a DFT type implementation that does not require the
data being anaylized to be a power of 2 in length would be superior
to a Cooley-Tukey implementation even if run time is a little
longer ...
--- In amibroker@xxxxxxxxx <mailto:amibroker%40yahoogroups.com> ps.com,
"Tomasz Janeczko" <groups@xxx>
wrote:
>
> For that you need Fourier transform and FFT is coming as a built
in function in 4.86
>
> Best regards,
> Tomasz Janeczko
> amibroker.com
> ----- Original Message -----
> From: "Fred" <ftonetti@xxx>
> To: <amibroker@xxxxxxxxx <mailto:amibroker%40yahoogroups.com> ps.com>
> Sent: Friday, October 06, 2006 3:48 AM
> Subject: [amibroker] Re: Polynomial Trendlines
>
>
> > Now if someone can take this method and/or AFL or at least
provide a
> > how to that takes us into Trigometric curve fitting and
extrapolation
> > i.e. the solution of simultaneous equations in the generalized
format
> > of a spectral model i.e. ...
> >
> > S ~ (a1 cos w1t + b1 sin w1t) + ... + (Am cos wm + bm sin wmt)
> >
> > Then we might have something fairly useful ...
> >
> > I suspect Gaussian Elimiation can be used for this as well, but
I
> > don't have the skill level to calculate the necessary matrix
entries
> > to get it down ...
> >
> > Any mathematicians out there ?
> >
> >
> > --- In amibroker@xxxxxxxxx <mailto:amibroker%40yahoogroups.com> ps.com,
"Fred" <ftonetti@> wrote:
> >>
> >> When stretch over enough data almost any order will become a
pseudo
> >> straight line ...
> >>
> >> By their nature a first order IS a straight line, 2nd U shape,
3rd
> >> order sine wave etc ...
> >>
> >> Try highlighting a SMALLER segment of data by using the
beginning
> > and
> >> ending range markers ...
> >>
> >>
> >> --- In amibroker@xxxxxxxxx <mailto:amibroker%40yahoogroups.com> ps.com,
"d_hanegan" <dhanegan@> wrote:
> >> >
> >> > Fred:
> >> >
> >> > Thanks for your posts and all of the information concerning
the
> >> > Polynomial Trendlines. When I run the code, I pretty much
just
> > get
> >> > a straight green line; it does not fit my data. I thought I
had
> >> > read all of the posts. Am I missing something?
> >> >
> >> > Thanks.
> >> >
> >> > Dan
> >> > --- In amibroker@xxxxxxxxx <mailto:amibroker%40yahoogroups.com>
ps.com, "Fred" <ftonetti@> wrote:
> >> > >
> >> > > Be AWARE ... that was a hand picked image ... if you play
with
> >> > > PolyFit you will see that sometimes data fits the
> > extrapolations,
> >> > > sometimes it doesn't.
> >> > >
> >> > > The higher the order, the flakier the extrapolations are
likely
> >> to
> >> > > become ...
> >> > >
> >> > > So ... Remember what it is ... a generator of an equation
in
> > the
> >> > form
> >> > >
> >> > > Y = a + bx + cx^2 + ... + nx^(n-1)
> >> > >
> >> > > Where the coeeficients were pick to fit the data.
> >> > >
> >> > > IMHO what PolyFit is, epecially with very high orders is a
very
> >> > good
> >> > > detrender of IN SAMPLE data, nothing more, nothing less ...
> > That
> >> > in
> >> > > and of itself is a useful tool ... Gaussian Elimination can
> > also
> >> > be
> >> > > the basis for some other things that are pretty decent when
the
> >> > order
> >> > > is kept fairly low i.e. 3 or 4 ...
> >> > >
> >> > > --- In amibroker@xxxxxxxxx <mailto:amibroker%40yahoogroups.com>
ps.com, "Ara Kaloustian" <ara1@>
> > wrote:
> >> > > >
> >> > > > Polynomial TrendlinesFred,
> >> > > >
> >> > > > There have been a lot of posting on this subject. Your
one
> >> > image
> >> > > however is a very powerful message of its potential.
> >> > > >
> >> > > > Now I have to go back and review all the post ... hoping
to
> >> find
> >> > a
> >> > > good reference to study.
> >> > > >
> >> > > > Anyone using it succesfully now?
> >> > > >
> >> > > > Ara
> >> > > > ----- Original Message -----
> >> > > > From: Fred Tonetti
> >> > > > To: amibroker@xxxxxxxxx <mailto:amibroker%40yahoogroups.com>
ps.com
> >> > > > Sent: Tuesday, October 03, 2006 3:32 PM
> >> > > > Subject: [amibroker] RE: Polynomial Trendlines
> >> > > >
> >> > > >
> >> > > > Oops .
> >> > > >
> >> > > >
> >> > > >
> >> > > > Meant to include this visual .
> >> > > >
> >> > > >
> >> > > >
> >> > > > Green is calculated . White is extrapolated .
> >> > > >
> >> > > >
> >> > > >
> >> > > >
> >> > > >
> >> > > >
> >> > > >
> >> > > > ----------------------------------------------------------
----
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> >
> > Please note that this group is for discussion between users only.
> >
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