Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference Hypothesis
Todd E. Clark
Federal Reserve Bank of Cleveland
Kenneth D. West
University of Wisconsin - Madison - Department of Economics; National Bureau of Economic Research (NBER)
FRB of Kansas City Working Paper No. 04-03
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.
Number of Pages in PDF File: 42
Keywords: Forecast Evaluation, Causality, Exchange Rates
JEL Classification: C52, C53, C12, F31working papers series
Date posted: August 5, 2004
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo1 in 1.844 seconds