Estimating the Variance of a Combined Forecast : Bootstrap-Based Approach

This paper considers bootstrap inference in model averaging for predictive regressions. We firstshow that a naïve bootstrap approach, which consists of stacking all residuals at time t into a vector, and then resampling these cross-sectional vectors of residuals over time is invalid in the context of model averaging. The naïve approach induces a bias-related term in the bootstrap variance of averaging estimators. We then propose and justify two general fixed-design residual-based bootstrap resampling approaches for model averaging in predicting regressions. In a local asymptotic framework, we show the validity of the bootstrap in estimating the variance of a combined forecast and the asymptotic covariance matrix of a combined parameter vector with fixed weights. Our two proposed methods - the general blocking-based residual resampling and the general dependent wild based residual resampling - can preserve nonparametrically the cross-sectional dependence between different models and the time series dependence in the errors simultaneously. The finite sample performance of these methods are assessed via Monte Carlo simulation. We illustrate our approach using an empirical study of the Taylor rule equation with 24 alternative specifications