Structural TS and recursive estimation
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 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._