A1235
Title: Time reversibility testing for stochastic processes
Authors: Hedvika Ranosova - Charles University (Czechia) [presenting]
Daniel Hlubinka - Univerzita Karlova (Czech Republic)
Abstract: Time reversibility, or its absence, represents a fundamental property of stochastic processes. Tests for the time reversibility of continuous-time stochastic processes are introduced. The Cramer-von Mises type test statistic is based on the distance between empirical characteristic functionals, which allows for testing equality of distributions. In addition to classical time reversibility, several alternative formulations are explored to include seemingly non-reversible processes, such as the standard Wiener process. The asymptotic behavior of the test statistic is derived given a sample of either independent or weakly dependent continuous functions. Due to the intricate asymptotic behavior of the test statistics, critical values are obtained through a resampling approach, via either a block bootstrap or a Bernoulli mixture. The effectiveness of the proposed tests is evaluated through simulation studies and further demonstrated using S&P 500 market data.
