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

A possible approach to test for conditional symmetry in time series regression models is discussed. To that end, the Bai and Ng test is utilized. The performance of some popular (unconditional) symmetry tests for observations when applied to regression residuals is also examined. The tests considered include the coefficient of skewness, a joint test of the third and fifth moments, the Runs test, the Wilcoxon signed-rank test and the Triples test. An easy-to-implement symmetric bootstrap procedure is proposed to calculate critical values for these tests. Consistency of the bootstrap procedure will be shown. A simple Monte Carlo experiment is conducted to explore the finite-sample properties of all the tests.