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I have some measures which seems to have some mean-reverting properties and I'm wondering whether they can be modeled as Ornstein-Uhlenbeck process (OU process). And actually I quite expect it because if so, the following work will be much easier because it seems that there has been many useful results of OU process.

But I don't know how to validate it. I used to think that I could calculate the KL distance but the probability density function seems to not have a closed form, so it can't be derived.

So I'm wondering how to test whether a series data follow an OU process?

Patrick Coulombe
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fisher
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1 Answers1

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You can fit the time series to an AR(1) process. The regression coefficients and autocorrelation function will give you an indication of its mean reversion properties.

The regression parameters of the AR(1) model can be mapped into an Ornstein Uhlenbeck process: the appendix of the Avellaneda and Lee paper has an example of the AR(1) $\rightarrow$ OU mapping

Felix
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