# time series in R

**Prof Brian D Ripley
**
ripley@stats.ox.ac.uk

*Tue, 20 Jul 1999 07:22:12 +0100 (BST)*

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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