Time Irreversible Copula-Based Markov Models

Economic and financial time series frequently exhibit time irreversible dynamics. For instance, there is considerable evidence of asymmetric fluctuations in many macroeconomic and financial variables, and certain game theoretic models of price determination predict asymmetric cycles in price series. 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. We illustrate the use of our time reversibility test and circulation density estimator by applying them to five years of Canadian gasoline price markup data.