Evaluating
Direct Multi-Step Forecasts
By Todd Clark and Michael McCracken
December 2001; Revised April 2005
RWP 01-14
Research Division
Federal Reserve Bank of Kansas City
Abstract
This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy and encompassing applied to direct, multi--step predictions from nested regression models. We first derive the asymptotic distributions of a set of tests of equal forecast accuracy and encompassing, showing that the tests have non-standard distributions that depend on the parameters of the data-generating process. We then conduct a range of Monte Carlo simulations to examine the finite-sample size and power of the tests. In these simulations, our asymptotic approximation yields good finite--sample size and power properties for some, but not all, of the tests; a bootstrap works reasonably well for all tests. The paper concludes with a reexamination of the predictive content of capacity utilization for core inflation.
Keywords: Prediction, long horizon, causality
JEL Codes: C53, C12, C52
Todd E. Clark is a vice president and economist at the Federal Reserve Bank of Kansas City. Michael W. McCracken is an assistant professor of economics at the University of Missouri-Columbia. Earlier versions of this paper were titled "Evaluating Long--Horizon Forecasts." The authors gratefully acknowledge the helpful comments of Lutz Kilian, David Rapach, Ken West, seminar participants at the Federal Reserve Bank of Kansas City, and participants at the 2001 MEG meetings. McCracken thanks LSU for financial support during work on a substantial portion of this paper. The views expressed herein are solely those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System.
todd.e.clark@kc.frb.org
mccrackenm@missouri.edu