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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