Serial Correlation in Contingency Tables - Helmut Elsinger (Oesterreichische Nationalbank (OeNB), 2020)
Pearson's chi-squared test for independence in two-way contingency tables is developed under the assumption of multinomial sampling. In this paper I consider the case where draws are not independent but exhibit serial dependence. I derive the asymptotic distribution and show that adjusting Pearson's statistic is simple and works reasonably well irrespective whether the processes are Markov chains or m-dependent. Moreover, I propose a test for independence that has a simple limiting distribution if at least one of the two processes is a Markov chain. For three-way tables I investigate the Cochrane-Mantel-Haenszel (CMH) statistic and show that there exists a closely related procedure that has power against a larger class of alternatives. This new statistic might be used to test whether a Markov chain is simple against the alternative of being a Markov chain of higher order. Monte Carlo experiments are used to illustrate the small sample properties.
Keywords: C12; C14; C52; 330; Goodness of Fit; Independence Tests; Cochrane-Mantel-Haenszel Test; Markov chain