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I am new to mean reversion, and I'd like to run an analysis on a fund (ts with monthly returns only) to see if mean reversion applies and if so, when it will happen.
Most of the examples I found focus on cointegrated securities. Ornstein-Uhlenbeck seems to be a popular model for mean reversion estimate. If someone could please provide me an example of applying OU model on a return-only time series or point me to the right direction, I will really appreciate it!
T, while not necessarily a direct answer to your question, I just wanted to offer a word of caution in applying a mean reversion model to security or fund returns.
In attempting to fit a mean reversion model to returns, you are implicitly stating that you believe that historical returns are good predictors of future returns. Although I don't know what your dataset is, this is generally not the case.
More likely to be mean reverting are the fundamentals underlying these returns. Using a financial markets example this might be something like multiples (P/E or EV/EBITDA).
But if you still wanted to run such a mean reversion analysis, I would recommend starting with a regression with a format similar to the following: use as your independent (x) variable the returns from period t and as your dependent (y) variable the returns from period t+1. If there is mean reversion you should see a negative resulting coefficient, although you should also check the fit of your result as well -- in keeping with my comments above, I would expect the fit to be poor, even if your coefficient is negative.
Hope this helps!
