Comparison of the Small Sample Power of the Chi-Square and Likelihood Ratio Tests of the Assumptions for Stochastic Models

Abstract When applying the Markov model, it is often assumed the transition matrix is stationary and of order one. This article considers the problem of applying the transformed likelihood ratio statistic and the contingency statistic to testing the assumptions of a particular order and of stationarity when the assumptions are not true. A Monte Carlo study of the small sample power of both these test statistics shows that if the true alpha level is kept equal for the two tests they have similar power. However, if the alpha level is set by reference to any standard table of the chi-square distribution the likelihood ratio statistic has larger power.