Time reversibility of stationary regular finite-state Markov chains

We propose an alternate parameterization of stationary regular finite-state Markov chains, and a decomposition of the parameter into time reversible and time irreversible parts. We demonstrate some useful properties of the decomposition, and propose an index for a certain type of time irreversibility, applicable to chains whose states are naturally ordered. Two empirical examples illustrate the use of the proposed parameter, decomposition and index. One, on gasoline price mark-ups, involves observed states. The other, on U.S. investment growth, features latent states.