Approximately Normal Tests for Equal Predictive Accuracy in Nested Models

FRB of Kansas City Working Paper No. RWP 05-05

45 Pages Posted: 22 Jan 2006

See all articles by Todd E. Clark

Todd E. Clark

Federal Reserve Bank of Cleveland

Kenneth D. West

University of Wisconsin - Madison - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 2 versions of this paper

Date Written: November 15, 2005

Abstract

Forecast evaluation often compares a parsimonious null model to a larger model that nests the null model. Under the null that the parsimonious model generates the data, the larger model introduces noise into its forecasts by estimating parameters whose population values are zero. We observe that the mean squared prediction error (MSPE) from the parsimonious model is therefore expected to be smaller than that of the larger model. We describe how to adjust MSPEs to account for this noise. We propose applying standard methods (West (1996)) to test whether the adjusted mean squared error difference is zero. We refer to nonstandard limiting distributions derived in Clark and McCracken (2001, 2005a) to argue that use of standard normal critical values will yield actual sizes close to, but a little less than, nominal size. Simulation evidence supports our recommended procedure.

Keywords: Forecast Evaluation, Causality, Nested Models

JEL Classification: C53, C52

Suggested Citation

Clark, Todd E. and West, Kenneth D., Approximately Normal Tests for Equal Predictive Accuracy in Nested Models (November 15, 2005). FRB of Kansas City Working Paper No. RWP 05-05, Available at SSRN: https://ssrn.com/abstract=874146 or http://dx.doi.org/10.2139/ssrn.874146

Todd E. Clark (Contact Author)

Federal Reserve Bank of Cleveland ( email )

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Kenneth D. West

University of Wisconsin - Madison - Department of Economics ( email )

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