Testing for embeddability by stationary reversible continuous-time Markov processes

Given an observation of a discrete-time process {Y-i, i = 0...n} assumed to be Markov, stationary, and time reversible, we develop a (conservative) te st procedure of embeddability by a continuous-time reversible Markov proces s. The test statistic is derived from a set of moment inequality restrictio ns implied by the spectral properties of such continuous-time processes. Mo st interesting is that the embeddability condition of interest is a direct extension of the well-known embeddability problem by a two-state Markov cha in. Empirical experiments show that the embeddability hypothesis is rejecte d more frequently for exchange rate daily data than for stock indices data.