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In this paper, we make two primary contributions to the econometric literature on time reversibility. First, we propose a new test of time reversibility, applicable to stationary Markov chains. Compared to existing tests, our test has the advantage of being consistent against arbitrary violations of reversibility. Second, we explain how a circulation density function may be used to characterize the nature of time irreversibility when it is present. We propose a copula-based estimator of the circulation density and verify that it is well behaved asymptotically under suitable regularity conditions. 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