Time-reversibility is a crucial feature in a majority of time-series models, while time-irreversibility is the rule rather than the exception in real data. Testing the null hypothesis of time-reversibility should therefore be an important step prior to the identification and estimation of most traditional time-series models. However, existing procedures mostly consist of testing necessary but not sufficient conditions, leading to under-rejection, or sufficient but not necessary conditions, leading to over-rejection of the null hypothesis of reversibility. Moreover, they are generally model-based. In contrast, the copula spectrum studied by Goto et al. (Ann. Statist. 2022, 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 the authors. This paper illustrates the performance of this test, with an illustration in the analysis of climate data.