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

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Johann Hibschman

Posts: 5
Registered: 4/16/07
Dynamic nonlinear regression, use SMC?
Posted: Apr 16, 2007 12:07 AM
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Hi all,

I'm interested in fitting dynamic nonlinear regression models to time
series data.

I have a complicated nonlinear functional form, with about 15-20
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
time-evolution 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
high-dimensional 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) high-level 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




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