Subject: Re: time series in R
From: Prof Brian D Ripley (email@example.com)
Date: Tue 20 Jul 1999 - 16:22:12 EST
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.
Isn't that the tail wagging the dog?
> No constant in the dft implies
> Periodogram = |dft|^2/(2*pi*T)
Why is the 2*pi there? It is in Bloomfield, but not Brockwell & Davis, for
example. And S-PLUS divides by the fequency to make the periodogram
estimate the spectral density.
> Phases in spectra also fall out if you take a +ve exponent in the dft.
But you have to decide which of series i and j gets the complex conjugate.
(Same issue with acfs: second relative to first or 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.
Consistent with whom?
-- Brian D. Ripley, firstname.lastname@example.org Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272860 (secr) Oxford OX1 3TG, UK Fax: +44 1865 272595
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