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

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  • Todd E. Clark
  • Kenneth D. West

Abstract

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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0305.

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Date of creation: Jan 2005
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Handle: RePEc:nbr:nberte:0305

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