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On a single time series one can run a Dickey-Fuller test to determine if the asset is mean reverting or at least has been mean reverting during your sample.

Is there a way to test for mean-reversion in a portfolio of assets? In other words is there a way to test if portfolio re-balancing would have offered statistically significant advantage?

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    $\begingroup$ You should read up on cointegration. Learn about the Engle-Granger test. If your portfolio weights are proportion to regression coefficients, then it should be similar to what you're talking about wrt testing for mean-reversion in a portfolio of assets. $\endgroup$
    – John
    Sep 25, 2015 at 18:42
  • $\begingroup$ Thanks @John. If you expand in a full answer with a little more background, I'm happy to give you credit. $\endgroup$
    – rhaskett
    Sep 28, 2015 at 15:40

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If two or more (I(1)) time series are cointegrated, then this means that you can find a linear combination of them that is mean-reverting. Thus, if you create a portfolio with weights that are proportional to this linear combination, then the portfolio returns will also be mean-reverting.

There is a large literature on cointegration and asset prices and many techniques to try to take advantage of this behavior in asset prices. For a small number of assets, you could fit a VAR or ECM. For larger dimensional problems, PCA is often used.

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