Improving Forecast Accuracy by Combining Recursive and Rolling Forecasts

By Todd E. Clark and Michael W. McCracken
October 2004 
RWP 04-10
Research Division 
Federal Reserve Bank of Kansas City 

Abstract

      This paper presents analytical, Monte Carlo, and empirical evidence on the effectiveness of combining recursive and rolling forecasts when linear predictive models are subject to structural change. We first provide a characterization of the bias-variance tradeoff faced when choosing between either the recursive and rolling schemes or a scalar convex combination of the two. From that, we derive pointwise optimal, time-varying and data-dependent observation windows and combining weights designed to minimize mean square forecast error. We then proceed to consider other methods of forecast combination, including Bayesian methods that shrink the rolling forecast to the recursive and Bayesian model averaging. Monte Carlo experiments and several empirical examples indicate that although the recursive scheme is often difficult to beat, when gains can be obtained, some form of shrinkage can often provide improvements in forecast accuracy relative to forecasts made using the recursive scheme or the rolling scheme with a fixed window width.

Keywords: Structural breaks, forecasting, model averaging

JEL Codes: C53, C12, C52

Todd Clark is vice president and economist at the Federal Reserve Bank of Kansas City and Michael McCracken is an assistant professor of Economics at the University of Missouri-Columbia. The authors gratefully acknowledge the excellent research assistance of Taisuke Nakata and helpful comments from Ulrich Muller, Peter Summers, Ken West, Jonathan Wright, seminar participants at the University of Virginia, the Board of Governors and the Federal Reserve Bank of Kansas City, and participants at the following meetings: MEG, Canadian Economic Association, SNDE, MEC, 2004 NBER Summer Institute, NBER/NSF Time Series Conference and the conference for young researchers on Forecasting in Time Series. 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.

Clark email:  todd.e.clark@kc.frb.org
McCracken email:  mccrackenm@missouri.edu

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