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I have a time-series with clear mean-reverting properties over some time-scale. I have a very long measurement of this series, so can see that, whilst it always reverts to a fixed mean, the fluctuations away from this are heavy tailed and skewed.

I am currently looking at modelling this as a mean-reverting process, driven by non-Gaussian noise. However, whilst I can speculate many different forms the noise should take, I do not know how to actually fit any parameters to my data.

Can anyone provide a reference for fitting such models, or a general walk through of how one might do this? I know the mean we revert to is clear from any inspection of the data, however how does one determine the memory parameter of such a process if it is not driven by Gaussian noise?

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