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

**From: **Adrian Trapletti (*Adrian.Trapletti@wu-wien.ac.at*)

**Date: **Tue 20 Jul 1999 - 22:53:28 EST

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Message-ID: <37947148.EB23277B@wu-wien.ac.at>

Martin Maechler wrote:

*>
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*> Something which should be discussed however is spectrum(0);
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*> Several of us think that S-plus does the wrong thing, at least in some
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*> cases. If demean=T (mean removed), should have periodogram(0) = 0,
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*> and maybe even spectrum(0) = 0 [and hence dB-spec. = -Inf ..]
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*> Another possibility would be to leave it NA
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*> and maybe provide methods for estimating it specifically, if desired.
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*>
*

I had a look at some of our Dep. books:

Brockwell&Davis: Periodogram normalization is n^{-1}, P(0)=0 for

demean=T.

spectrum(0) should be estimated by not using P(0) (Remark 2, p. 353). In

general

S(0) \neq 0.

Shiryaev, Probability: Per. norm. is (2*pi*n)^{-1}, P(0)=0 for demean=T.

Priestley, Spectral Analysis... : Periodogram normalization is

(n/2)^{-1}, P(0)=0

for demean=T, p. 395. For continuous spectra he defines a "modified

Periodogram",pp. 416, 417, where the normalization is as in Shiryaev.

All the

spectrum estimation is done with the mod. Period.

Hannan, Multiple Time Series: Normalization is (n/2)^{-1}.

Koopmans: Spectral Analysis of TS: Norm. is (2*pi*n)^{-1}.

It seems that (2*pi*n)^{-1} is the version which is mostly used, since

it makes no

further normalization necessary, e.g., for smoothing the periodogram.

P(0)=0 is

obvious. And \hat{spectrum}(0) = 0 is definitely a very bad estimator.

Adrian

-- Adrian Trapletti, Vienna University of Economics and Business Administration, Augasse 2-6, A-1090 Vienna, Austria Phone: ++43 1 31336 4561, Fax: ++43 1 31336 708, Email: adrian.trapletti@wu-wien.ac.at-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-devel mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-devel-request@stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._

**Next message:**Martyn Plummer: "RE: time series in R"**Previous message:**Prof Brian Ripley: "RE: time series in R"**Maybe in reply to:**Prof Brian D Ripley: "time series in R"**Maybe reply:**Adrian Trapletti: "Re: time series in R"

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