A Bootstrap Test for Symmetry of Dependent Data Based on a Kolmogorov–Smirnov Type Statistic

This article considers a nonparametric test for symmetry of the marginal law of a stationary stochastic process based on a Kolmogorov–Smirnov type statistic. Since the asymptotic null distribution of this statistic depends on the unknown law of the data, P-values and critical values for the test are estimated by means of a symmetric sieve bootstrap procedure based on residual resampling from an autoregressive approximation to the given process. The small-sample performance of the sieve bootstrap test is assessed by means of Monte Carlo experiments, which show that the test performs satisfactorily in terms of null rejection rates and power, although it does tend to be somewhat conservative for time series of relatively short length.