Premium
Test Statistics for Simple MARKOV Chains. A Monte Carlo Study
Author(s) -
Bedall Fritz K.
Publication year - 1978
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710200106
Subject(s) - markov chain , markov chain monte carlo , test statistic , statistics , mathematics , series (stratigraphy) , statistic , monte carlo method , simple (philosophy) , statistical hypothesis testing , computer science , algorithm , paleontology , philosophy , epistemology , biology
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 X 2 ‐distributed. The test statistic SS ( F (p) = Xb ) for evaluation of the lack of fit of the model also follows a X 2 ‐distribution when a simple MARKOV chain ∼ is used instead of the observed time series ∼ can be determined by simply iterating the original GSK algorithm.