time series in R
Martin Maechler <email@example.com>
Tue, 20 Jul 1999 11:32:37 +0200
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 > >
>> > 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
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
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.
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