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Three different notions of time reversibility of stochastic processes are introduced. Based on a random sample, we construct a statistical test for each version of time reversibility without any distributional or moment assumptions. The characteristic functional is utilized in the Cramér-von Mises test statistic with a pre-chosen weighting measure. Several simulations illustrate the performance of the proposed test.

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Non-Parametric Testing of Time Reversibility in Functional Data

  • 会议论文

  • 发表日期：

    2025年

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  • Hedvika Ranošová,
  • Daniel Hlubinka

摘要

Three different notions of time reversibility of stochastic processes are introduced. Based on a random sample, we construct a statistical test for each version of time reversibility without any distributional or moment assumptions. The characteristic functional is utilized in the Cramér-von Mises test statistic with a pre-chosen weighting measure. Several simulations illustrate the performance of the proposed test.