Jutaporn Jindasawat

Testing the order of a Markov chain model

Discrete state series are often modelled using the Markov chains. To access the most appropriate fit, the data can normally be displayed and analysed based on standard method, i.e. a contingency table Chi-square test and its extensions, by assuming constant of the transition probabilities along the sequences. However, in many plausible scenarios, the parameterization of such processes the number of parameters increases geometrically with the order and the heterogeneity can be undetected; therefore, it is less likely to achieve a validity of the stationary distribution assumption. To obtain an efficient way of testing the Markovian model, a possible alternative approach based on the run length is investigated. The run length can be defined as a length of the same consecutive values. Its distribution can be derived by the probability theory. The result of these are compared to the power of the standard Chi-square test when the sequences studied are independent and first-order Markov chain and either homogeneous or non-homogeneous.