Message-ID: <Pine.LNX.4.31.0208051032400.23422-100000@gannet.stats>
Date: 2002-08-05T09:36:23Z
From: Brian Ripley
Subject: Structural TS and recursive estimation
In-Reply-To: <OF7013A897.63F3A2A8-ONC1256C0C.002E510D@fr>
On Mon, 5 Aug 2002 julien.ruiz at airfrance.fr wrote:
> Since my question is quite theorical, I am not sure whether it is the right
> place to ask, but anyway...
> I am working on time series and I looked at some way to fit my data through
> arima models.
> Since these data are updated frequently, I was looking at a way to update
> the model "on line" (to get a kind of recursive estimation)
> So the next step was to express the arima models as state-space
> (structural) models.
> The idea was to use the recursive formulaes of a Kalman Filter, in order to
> get an estimation of the kind of the recursive least square.
> But it seems to me that the estimation of these structural models requires
> a likelihood maximization which is not recursive.
>
> So my question is :
> In a structural model, can the likelihood maximization be done recursively
> ?
>
> Upon what I read in 2 first articles of the 2/2 issue of R News, I don't
> think it is done this way in R.
1) ARIMA fitting *is* done via state-space models, but structural models
are something different.
2) You can't (in general) do ML estimation of the parameters of a
state-space model recursively. Nor is that what recursive least squares
estimates.
For more details, see the references in the article you mention,
especially the Durbin & Koopman book.
--
Brian D. Ripley, ripley at 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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