Time-reversibility is a crucial feature of many time series models, while time-irreversibility is the rule rather than the exception in real-life data. Testing the null hypothesis of time-reversibilty, therefore, should be an important step preliminary to the identification and estimation of most traditional time-series models. Existing procedures, however, mostly consist of testing necessary but not sufficient conditions, leading to under-rejection, or sufficient but non-necessary ones, which leads to over-rejection. Moreover, they generally are model-besed. In contrast, the copula spectrum studied by Goto et al. ($\textit{Ann. Statist.}$ 2022, $\textbf{50}$: 3563--3591) allows for a model-free necessary and sufficient time-reversibility condition. A test based on this copula-spectrum-based characterization has been proposed by authors. This paper illustrates the performance of this test, with an illustration in the analysis of climatic data.

翻译：时间可逆性是许多时间序列模型的关键特征，而现实数据中时间不可逆性才是常态而非例外。因此，检验时间可逆性的原假设应成为识别和估计大多数传统时间序列模型前的重要步骤。然而，现有检验方法大多仅检验必要非充分条件（导致拒绝不足），或充分非必要条件（导致过度拒绝），且通常依赖于特定模型。相比之下，Goto等人（《统计年鉴》2022年第50卷：3563-3591）研究的联结谱提供了一种无模型的、必要且充分的时间可逆性条件。作者已基于此联结谱表征提出了一种检验方法。本文通过气候数据分析的实例，展示了该检验方法的性能。