Forecasting under Structural Breaks Using Improved Weighted Estimation

In forecasting a time series containing a structural break, it is important to determine how much weight can be given to the observations prior to the time when the break occurred. In this context, Pesaran et al. (2013) (PPP) proposed a weighted least squares estimator by giving different weights to observations before and after a break point for forecasting out-of-sample. We revisit their approach by introducing an improved weighted generalized least squares estimator (WGLS) using a weight (kernel) function to give different weights to observations before and after a break. The kernel weight is estimated by cross-validation rather than analytically derived from a parametric model as in PPP. Therefore, the WGLS estimator facilitates implementation of the PPP method for the optimal use of the pre-break and post-break sample observations without having to derive the parametric weights which may be misspecified. We show that the kernel weight estimated by cross-validation is asymptotically optimal in the sense of Li (1987). Monte Carlo simulations and an empirical application to forecasting equity premium are provided for verification and illustration.