Test Statistics for Simple MARKOV Chains. A Monte Carlo Study
Biometrical Journal, 20 (1):
41--49 (1978)Abstract
The statistical method for the analysis of frequency tables which has been published by GRIZZLE, STARMER, and KOCH (1969) is outlined for the case of linear functions of relative frequencies. Its use for the analysis of aggregate time series data under the model of simple MARKOV chains is suggested. Weighty objections against the resulting test statistics were grounds for the planning and performance of a Monte Carlo study. The results of the study demonstrated that the test statistic SS (Cb=0) which is used for the comparison of different MARKOV chains is in fact X2-distributed. The test statistic SS (F(p) =Xb) for evaluation of the lack of fit of the model also follows a X2-distribution when a simple MARKOV chain is used instead of the observed time series can be determined by simply iterating the original GSK algorithm.