NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference

Todd E. Clark, Kenneth D. West

NBER Technical Working Paper No. 305
Issued in January 2005
NBER Program(s):   TWP   AP   IFM

We consider using out-of-sample mean squared prediction errors (MSPEs) to evaluate the null that a given series follows a zero mean martingale difference against the alternative that it is linearly predictable. Under the null of no predictability, the population MSPE of the null "no change" model equals that of the linear alternative. We show analytically and via simulations that despite this equality, the alternative model's sample MSPE is expected to be greater than the null's. For rolling regression estimators of the alternative model's parameters, we propose and evaluate an asymptotically normal test that properly accounts for the upward shift of the sample MSPE of the alternative model. Our simulations indicate that our proposed procedure works well.

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Document Object Identifier (DOI): 10.3386/t0305

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