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Tests of Equal Forecast Accuracy and Encompassing for Nested Models 
Todd E. Clark 
Michael W. McCracken 
October 1999 
Last Revised: November 2000 
RWP 99-11 
Research Division 
Federal Reserve Bank of Kansas City 
    Abstract
We examine the asymptotic and finite-sample properties of tests for equal forecast accuracy and encompassing applied to 1-step ahead forecasts from nested parametric models. We first derive the asymptotic distributions of two standard tests and one new test of encompassing. Tables of asymptotically valid critical values are provided. Monte Carlo methods are then used to evaluate the size and power of the tests of equal forecast accuracy and encompassing. The simulations indicate that post-sample tests can be reasonably well sized. Of the post-sample tests considered, the encompassing test proposed in this paper is the most powerful. We conclude with an empirical application regarding the predictive content of unemployment for inflation. 
Todd E. Clark is an assistant vice president and economist at the Federal Reserve Bank of Kansas City. Michael W. McCracken is an assistant professor of economics at Louisiana State University. The authors thank Hilary Croke for valuable research assistance and Charles Engel, Lutz Kilian, Norm Swanson, Dek Terrell, Ken West, and seminar participants at Penn State and the University of Michigan for helpful comments. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System. 
Clark e-mail: todd.e.clark@kc.frb.org
McCracken e-mail: mccrac@unix1.sncc.lsu.edu
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