[18675] in s-news-athena
Re: [S] Time Series Arima Models
daemon@ATHENA.MIT.EDU (Prof Brian D Ripley)
Tue Jul 20 09:36:48 1999
Date: Tue, 20 Jul 1999 14:32:55 +0100 (BST)
From: Prof Brian D Ripley <ripley@stats.ox.ac.uk>
To: Mark Lehr <mlehr@pacbell.net>
Cc: S-news@wubios.wustl.edu
In-Reply-To: <199907192229.PAA19549@mail-gw3.pacbell.net>
Message-Id: <Pine.GSO.4.05.9907201426250.6129-100000@auk.stats>
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On Mon, 19 Jul 1999, Mark Lehr wrote:
> Help
> For those of you who use the Splus Function
> ARIMA.MLE
> there are many outputs from this routine but
> one seems to be lacking. The time series model
> returned provides the AR and MA coefficient estimates
> with their covariance matrix.
> Also returned is the innovation variance but is
> there a variance of this term calculated. In other
> words the variance of the variance. It is an
> estimated parameter just like the AR and MA
> coefficients and I would expect this as well. Maybe
When you estimate a regression, you get a residual
variance, but no variance for (the estimator of) that term.
This is exactly the same (just an autoregression, not a regression).
As far as I know the same reasoning applies (it certainly does
in the AR(p) case):
n s^2/sigma^2 ~ chisq_n
where n is approximately the length of the series, and this gives
you an approximate variance for s^2. As in regression, the
estimators of the coefficients and s^2 are approximately uncorrelated.
If this matters, please check the asymptotic theory in, for example,
Brockwell & Davis.
--
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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