Variable Selection and Forecasting in High Dimensional Linear Regressions with Structural Breaks

This paper is concerned with the problem of variable selection and forecasting in the presence of parameter instability. There are a number of approaches proposed for forecasting in the presence of breaks, including the use of rolling windows and exponential down-weighting. However, these studies start with a given model specification and do not consider the problem of variable selection, which is complicated by time variations in the effects of signal variables. In this study we investigate whether or not we should use weighted observations at the variable selection stage in the presence of structural breaks, particularly when the number of potential covariates is large. Amongst the extant variable selection approaches we focus on the recently developed One Covariate at a time Multiple Testing (OCMT) method. This procedure allows a natural distinction between the selection and forecasting stages. We establish three main theorems on selection, estimation post selection and in-sample fit. These theorems provide justification for using the full (not down-weighted) sample at the selection stage of OCMT and down-weighting of observations only at the forecasting stage (if needed). The benefits of the proposed method are illustrated by empirical applications to forecasting output growths and stock market returns