**Subject: **Re: time series in R

**From: **Martin Maechler (*maechler@stat.math.ethz.ch*)

**Date: **Tue 20 Jul 1999 - 19:32:37 EST

**Next message:**Peter Dalgaard BSA: "Re: 0.65/AIX"**Previous message:**Martyn Plummer: "RE: time series in R"**In reply to:**Prof Brian D Ripley: "Re: time series in R"**Next in thread:**Martyn Plummer: "Re: time series in R"**Reply:**Martin Maechler: "Re: time series in R"

Message-Id: <199907200932.LAA25315@sophie.ethz.ch>

* BDR> On Tue, 20 Jul 1999, Ross Ihaka wrote:
*

* >> On Mon, 19 Jul 1999, Prof Brian D Ripley wrote:
*

* >>
*

* >> > > 3. On the definition question: The existing FFT implementation >
*

* >> > uses a particular definition for the discrete transform which > >
*

* >> is pretty standard. (Edwards "Fourier Series", Brillinger > > "Time
*

* >> Series" etc.) Using another definition may complicate > >
*

* >> documentation.
*

* >> >
*

* >> > That's the simple part. But what is the divisor in the
*

* >> periodogram? Which > way do lags go in acfs of bivariate series, and
*

* >> which sign is the phase for > bivariate spectra?
*

* >>
*

* >> Once you settle the forward discrete transform much of this is
*

* >> settled.
*

* BDR> Isn't that the tail wagging the dog?
*

I think Ross meant to say that fft()'s definition can't (shouldn't) be changed

anymore, and I agree on that [and that *is* S compatible anyway].

* >> No constant in the dft implies Periodogram = |dft|^2/(2*pi*T)
*

* BDR> Why is the 2*pi there? It is in Bloomfield, but not Brockwell &
*

* BDR> Davis, for example. And S-PLUS divides by the fequency to make the
*

* BDR> periodogram estimate the spectral density.
*

We have to decide if we go for S-plus compatibility here, see below.

* >> Phases in spectra also fall out if you take a +ve exponent in the
*

* >> dft.
*

* >>
*

* BDR> But you have to decide which of series i and j gets the complex
*

* BDR> conjugate. (Same issue with acfs: second relative to first or
*

* BDR> first relative to second? It's like defining `lags'.)
*

* >> I don't much mind about these choices, but its probably a good idea
*

* >> to be consistent.
*

* BDR> Consistent with whom?
*

Mostly "with your own notation and definitions",

maybe even ``consistent with one book's author''.

I'd prefer Brockwell & Davis,

however I agree with Brian that S compatibility -- to some extent -- is a

goal here; on the other hand, S-plus uses definitions that are not widely

used in standard texts (my limited experience).

This really must must be settled now.

If nobody can show why S-plus definitions are `wrong by design' here,

I'd vote for adopting them, inspite of all...

[if only to keep V&R's chapter on time-series coherent :-)]

Something which should be discussed however is spectrum(0);

Several of us think that S-plus does the wrong thing, at least in some

cases. If demean=T (mean removed), should have periodogram(0) = 0,

and maybe even spectrum(0) = 0 [and hence dB-spec. = -Inf ..]

Another possibility would be to leave it NA

and maybe provide methods for estimating it specifically, if desired.

Martin

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**Next message:**Peter Dalgaard BSA: "Re: 0.65/AIX"**Previous message:**Martyn Plummer: "RE: time series in R"**In reply to:**Prof Brian D Ripley: "Re: time series in R"**Next in thread:**Martyn Plummer: "Re: time series in R"**Reply:**Martin Maechler: "Re: time series in R"

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