Multistep forecasting in the presence of location shifts

Abstract

This paper studies the properties of iterated and direct multistep forecasting techniques in the presence of in-sample location shifts (breaks in the mean). It also considers the interactions of these techniques with multistep intercept corrections that are designed to exhibit robustness to such shifts. In a local-asymptotic parameterization of the probability of breaks, we provide analytical expressions for forecast biases and mean-square forecast errors. We also provide simulations which show that breaks provide a rationale for using methods other than iterated multistep techniques. In particular, we study the relationships between the relative accuracy of the methods and the forecast horizon, the sample size and the timing of the shifts. We show that direct multistep forecasting provides forecasts that are relatively robust to breaks, and that its benefits increase with the forecast horizon. In an empirical application, we revisit an oft-used dataset of G7 macroeconomic series and corroborate our theoretical results.