Modified Parsimonious Model Averaging Under Heteroscedasticity

ABSTRACT We propose a modified parsimonious model averaging method under heteroscedasticity by incorporating the covariance matrix into the weight choice criterion. We demonstrate that when correctly specified models exist in the candidate model set, the weight assigned to the smallest correct model tends to 1. This leads to the consistency of variable selection and the asymptotic normality of the modified parsimonious model averaging estimator. Furthermore, we prove its asymptotic optimality within the given weight space when all candidate models are misspecified. Numerical simulations indicate that, in the presence of heteroscedasticity, the modified parsimonious model averaging estimator outperforms the unmodified version in terms of prediction accuracy. As an illustration example, we apply this method to predict housing rental prices in Fengtai District, Beijing.