[R] Structural TS and recursive estimation

ripley@stats.ox.ac.uk ripley at stats.ox.ac.uk
Mon Aug 5 11:36:23 CEST 2002

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

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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