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September 19

stochastic curve fitting

I have activity time series data of animal activity for various parameters (speed, curvature, etc.) I would like find stochastic models (maybe a Markov chain?) that would "explain" or "be consistent with" the time series, i.e. finding the coefficients or parameters of such a consistent model. Any elegant model would be a good start. Is there a way to fit a stochastic model to time series data, just like one would fit a regression curve to data? (Maybe by running the stochastic model n times to get statistically-determined parameters?) The parameters would quantify noise compared to determinism, or maybe explain a noisy decay profile.

The original motivation was to find more sophisticated parameters than a time constant to explain the decay profile of animal activity following a stimulus, because I have a feeling that k in y' = -ky would in fact get smaller (approach zero) as y approached a baseline value (since activity doesn't decay to zero as exponential decay would imply, but reach a baseline). 128.143.218.78 (talk) 08:36, 19 September 2012 (UTC)[reply]

You will find some useful information at time series analysis. SemanticMantis (talk) 15:10, 19 September 2012 (UTC)[reply]

For instance, the Box-Jenkins methodology might be useful, though I caution that it would take a fair bit of math/stat/computer prowess to do all that correctly. SemanticMantis (talk) 02:18, 20 September 2012 (UTC)[reply]