A New Nonparametric Combination Forecasting with Structural Breaks

Abstract

This paper proposes a new nonparametric forecasting procedure based on a weighted local linear estimator for a nonparametric model with structural breaks. The proposed method assigns a weight based on both the distance of observations to the predictor covariates and their location in time and the weight is chosen using multifold forward-validation to account for time series data. We investigate the asymptotic properties of the proposed estimator and show that the weight estimated by the multifold forward-validation is asymptotically optimal in the sense of achieving the lowest possible out-of-sample prediction risk. Additionally, a nonparametric method is adopted to estimate the break date and the proposed approach allows for different features of predictors before and after break. A Monte Carlo simulation study is conducted to provide evidence for the forecasting outperformance of the proposed method over the regular nonparametric post-break and full-sample estimators. Finally, an empirical application to volatility forecasting compares several popular parametric and nonparametric methods, including the proposed weighted local linear estimator, demonstrating its superiority over other alternative methods.