Estimation, Hypothesis Testing and Parameter Correlation for Markov Chains

In this report we will discuss four problems in statistical inference for Markov chains. Specifically, techniques are described to do the following: 1) estimate the transition probabilities of first- and second-order stationary Markov chains; 2) test the hypothesis that a stationary Markov chain is of first order against the alternate hypothesis that the chain is of second order; and 3) test the hypothesis that a first-order Markov chain has stationary transition probabilities against the alternate hypothesis that the transition probabilities are not stationary. A technique is also developed which can be used in testing to determine whether two parameters of a single electronic component drift independently of each other. The results of these tests are used to draw some inference about continuous-time Markov processes.