Conditional Skewness, Kurtosis, and Density Specification Testing: Moment-Based versus Nonparametric Tests

Abstract

Recently, there has been much interest in modeling time-varying higher-order conditional moments in the density estimation context. These studies employ a moment-based methodology to test their specification of higher-order conditional moments. We compare the size and power of these moment-based tests with the size and power of a recently developed set of nonparametric tests. The results show that the moment-based tests have good size only for conditional skewness and have a large size distortion when all the moment conditions are tested jointly and used as an overall specification test. The nonparametric tests have a slight size distortion for conditional higher moments, which can be eliminated. The power of the nonparametric tests for detecting overall misspecification and lack of dynamics in the conditional higher moments is better than the power of the moment-based tests.