A bootstrap approach to test the conditional symmetry in time series models

Abstract

This paper discusses how to test for conditional symmetry in time seriesregression models. To that end, we utilize the Bai and Ng test. We also examinethe performance of some popular (unconditional) symmetry tests for observationswhen applied to regression residuals. The tests considered include the coeficientof skewness, a joint test of the third and fifth moments, the Runs test, the Wilcoxonsigned-rank test and the Triples test. An easy-to-implement symmetric bootstrapprocedure is proposed to calculate critical values for these tests. Consistency of thebootstrap procedure will be shown. A simple Monte Carlo experiment isconducted to explore the finite-sample properties of all the tests