Markov chain test for time dependence and homogeneity: An analytical and empirical evaluation

This paper presents a complete framework for the testing procedure based on statistical theory of Markov chains. First, based on this methodology, an analytical evaluation of the Markov representation of time series is undertaken. It is shown that there is a one-to-one correspondence between the AR(1) parameter and the transition probability matrix of the Markov representation of that series. Using this result, we derived an analytical measure of the statistical power of the Markov chain test to detect structural break in the data. We later used Monte Carlo experiments to examine the finite-sample properties of the Markov chain time dependence and homogeneity tests taking the circular dependence between the two into account. The results showed that under the null hypothesis of an i.i.d. random walk, the empirical size of the Markov chain time dependence test is close to its nominal value irrespective of the sample size and the number of states. Unlike the size calculations, sample size matters in power calculations. Under the alternative integrated AR(1) and AR(2) processes, the power of the Markov chain test increases rapidly with the number of observations. Finally, the Monte Carlo results show that Markov chain test does not have much desirable properties as a test of time homogeneity. The size of the Markov chain test for time homogeneity is lower than its nominal value, when the underlying series is a homogeneous random walk. For time homogenous integrated AR(1) process with a low AR(1) parameter, size distortion of the Markov chain test is still low. However, as the sum of autoregressive parameters increases away from zero, the number of false rejections of the time homogeneity hypothesis increases as well. Finally, the power of Markov chain time homogeneity test increases with the sample size and with the increase in autoregressive parameters. However, in statistical power calculations Markov chain test does not perform better than structural break tests. JEL Classification: C12, C15, C22.