From ripley@stats.ox.ac.uk  Tue Jul 20 07:22:12 1999
From: ripley@stats.ox.ac.uk (Prof Brian D Ripley)
Date: Tue, 20 Jul 1999 07:22:12 +0100 (BST)
Subject: time series in R
In-Reply-To: <Pine.GSO.4.10.9907201215490.18298-100000@stat1.stat.auckland.ac.nz>
Message-ID: <Pine.GSO.4.05.9907200716520.5672-100000@auk.stats>

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,                  ripley@stats.ox.ac.uk
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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time series in R
Prof Brian D Ripley