David,
I appreciate all the comments (esp. #3). I was headed in that direction, but
this comment has put a spotlight on my search, so to speak. Definitely
helpful -- thanks!
regards,
p
----- Original Message -----
From: "David Jones" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, May 11, 2004 5:52 AM
Subject: Re: [edstat] higher order statistics and phase information
> p s upadrashta wrote:
> > Thanks, i'll look into this book. I wanted to send a personal email
> > to your address: [EMAIL PROTECTED] but it was returned -- saying that
> > "mail delivery subsystem failure: user not found". Not sure why.
> >
> > Can you provide some intuition for what polyspectra are (in words)
> to
> > get me started?
> >
> > thanks,
> > p
> >
>
> Your later try by e-mail did work after removing the anti-spam bit. I
> think its probably better to continue discussion in the newsgroup (but
> possibly sci.stat.math would suit better), so that others can join in.
> So I am adding-in your e-mail to me here ...
>
> >Hi,
> >I looked up polyspectra in that book, they appear to be simply
> integral transforms
> > applied to higher-order moments about the mean; e.g., the bispectrum
> is the FT
> > of the third-order moment, E{[x(t)-mu_x][x(t-tau1) -
> mu_x][x(t-tau2) - mu_x]} (referred to as
> >E{...} from now on...).
> >
> >I don't see what relationship the third-order or fourth-order
> structure has with respect
> > to the phase information. I realize that the
> >E{...} when projected onto the i*sin() part of (e^iwt) is the phase
> component.
> > Can you please provide some intuition on this, or
> >suggest a "dumbed down" book on bispectra that might explain it?
> >
> >my understanding so far: The bispectrum (i.e., using E{...} above)
> appears to be
> > the interaction between a sin wave with freq 1
> >and sin wave with freq 2 within the original time-series, x(t).
> Presumably,
> > the "real" part will be the extent of this interaction, but
> >what does the "imaginary" component represent??
> >
> >thanks in advance,
> >p
>
> (1) I think the book by Priestley is the simplest I know. However, you
> may find use for the material in the book "Time Series: Data Analysis
> and Theory" by D.R Brillinger, Holt, Rinehart and Winston Inc, 1975.
> Maybe others can suggest later publications on the topic?
>
> (2) My knowledge of interpreting spectra and polyspectra is very
> limited. I suggested polyspectra because there is a direct
> correspondence between these and all the joint higher order moments of
> a time-series. Thus you have a similar (time domain) to (frequency
> domain) correspondence for higher monments as arises for second-order
> moments.
>
> (3) It seems that phase information is not treated very well in
> typical time-series analysis theory, apart from the cases involving
> more than one series. This seems to be because of the theory of
> spectral representation of time series which says that the phase is
> uniformly distributed and thus "uninteresting". So there may be room
> for something new here.
>
> David Jones
>
>
> .
> .
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