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Using out-of-sample mean squared prediction errors to test the Martingale difference hypothesis

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Author Info
Todd E. Clark
Kenneth D. West

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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 zero 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. 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 Federal Reserve Bank of Kansas City in its series Research Working Paper with number RWP 04-03.

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Date of creation: 2004
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Handle: RePEc:fip:fedkrw:rwp04-03

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Keywords: Foreign exchange rates;

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  2. Todd E. Clark & Michael W. McCracken, 2001. "Evaluating long-horizon forecasts," Research Working Paper RWP 01-14, Federal Reserve Bank of Kansas City. [Downloadable!]
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  5. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October. [Downloadable!] (restricted)
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  32. Norman R. Swanson, 2000. "An Out of Sample Test for Granger Causality," Econometric Society World Congress 2000 Contributed Papers 0362, Econometric Society. [Downloadable!]
  33. Nelson, Charles R & Kim, Myung J, 1993. " Predictable Stock Returns: The Role of Small Sample Bias," Journal of Finance, American Finance Association, vol. 48(2), pages 641-61, June. [Downloadable!] (restricted)
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