Improving Forecast Accuracy by Combining Recursive and Rolling Forecasts*

Abstract

This article presents analytical, Monte Carlo, and empirical evidence on combining recursive and rolling forecasts when linear predictive models are subject to structural change. Using a characterization of the bias-variance trade-off faced when choosing between either the recursive and rolling schemes or a scalar convex combination of the two, we derive optimal observation windows and combining weights designed to minimize mean square forecast error. Monte Carlo experiments and several empirical examples indicate that combination can often provide improvements in forecast accuracy relative to forecasts made using the recursive scheme or the rolling scheme with a fixed window width. Copyright � (2009) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association No claim to original US government works .

Can currency-based risk factors help forecast exchange rates?

“…Recently, Clark and McCracken (2009) show a procedure to compute the optimal forecast combination weights θ and p1´θq for the recursive and rolling forecasting schemes, respectively. We follow their methodology and obtain three values for the combination weight θ.…”

“…The one-month ahead combined forecasts of exchange rate returns for individual currencies are from recursive regressions with a eight-year starting expanding window and rolling regressions with a eight-year window using weights θ " 0.92 and p1´θq " 0.08, respectively, and unconditional expectations of risk factors. The weights for combining the rolling and recursive scheme forecasts are computed as in Clark and McCracken (2009). The null hypothesis is that the competing model and the RWD provide equally accurate forecasts (i.e., U k i " 1), while the alternative hypothesis is that the competing model is more accurate than the RWD (i.e., U k i ă 1).…”

Measuring Interconnectedness between Financial Institutions with Bayesian Time-Varying Vector Autoregressions

“…Moreover, the rolling window approach is known to be susceptible to outliers because, in small subsamples, these have a larger impact on estimates (Zivot and Wang (2006)). On the other hand, choosing longer windows will lead to estimates that are less 1 reactive to change, biasing results towards time-invariant connections (Clark and McCracken (2009)). The rolling window approach will always involve a trade-off between the precision and reactivity of estimates of interconnectedness.…”

Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity

“…To save space, we present the results only of the rolling forecasting approach, which is preferable, given the possibility of the presence of structural breaks (see, e.g., [68]). …”