Forecasting Under Structural Breaks Using Improved Weighted Estimation
提出一种改进的加权广义最小二乘估计量，通过交叉验证估计核权重来优化结构突变前后的样本使用，避免参数权重误设，蒙特卡洛模拟和股票溢价预测验证了其有效性。
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 prebreak and postbreak 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.