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For every day in a year, I have the return on an asset and the CAPM estimation for the return.

I want to measure the average difference between the set of returns and set of estimations.

So far, I have applied Chi Squared but I want to use other measurements as well.

Is there anything equivalent to Chi_Squared which is normally used for measuring the difference between returns and estimations of a financial model?

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You can apply the Kolmogorov-Smirnov test. I simply quote from the entry:

"The two-sample K–S test is one of the most useful and general nonparametric methods for comparing two samples, as it is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples."

There is an R-implementation too.

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