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Topic:
Dynamic nonlinear regression, use SMC?
Replies:
2
Last Post:
Apr 20, 2007 1:03 PM




Dynamic nonlinear regression, use SMC?
Posted:
Apr 16, 2007 12:07 AM


Hi all,
I'm interested in fitting dynamic nonlinear regression models to time series data.
I have a complicated nonlinear functional form, with about 1520 parameters. I want to allow the parameters to evolve over time, both as a way to improve the fit and as a way to better understand the system. I don't have any structured parameter evolution, just random drift. I'd like to find a way to do a sequential analysis of the data, so that I can reasonably update the current state of the system given additional data.
I have a lot of data, several hundred megabytes in a relatively condensed format. I get a large block of data every month, so each timeevolution would have more the feel of a regression/minimization calculation than a straightforward Kalman filter "sliding" of the posterior distribution. (This is vague because I'm not sure if it is correct or even makes sense. I have a lot of observations every time step, which seems unusual in the literature.)
Now, I have Harrison & West's _Bayesian Forecasting and Dynamic Models_, which provides a great description of the linear case and an overview of the nonlinear case, but doesn't go much into the details, and seems to imply that there is no terribly good solution for the highdimensional case.
I was wondering what the current state of the art was. I've seen references to particle filter and sequential monte carlo methods, which seem interesting. However, I don't know a thing about them, beyond reading some (very) highlevel overviews. I was wondering:
1) Is this an appropriate direction for me to be researching? Are there any other keywords that I should be searching for?
2) What are the best references to read, to better understand this?
3) Does anyone have software packages to recommend, so I can experiment with these techniques? (I tend to prefer R, but I also use SAS and can dig up Matlab if I have to. In general, anything goes.)
As far as references go, I've seen citations of _Sequential Monte Carlo Methods in Practice_, ed. by Arnaud Doucet, Nando de Freitas, Neil Gordon (2001). Is this still considered a good summary of the field, or is there a better reference out there? (Shockingly, 2001 is starting to be a long time ago.)
Thanks for any advice,
Johann



