Serial Correlation in Contingency Tables (Helmut Elsinger)

Helmut Elsinger

Working Papers from Oesterreichische Nationalbank (Austrian Central Bank)

Abstract: 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: Goodness of Fit; Independence Tests; Cochrane-Mantel-Haenszel Test; Markov chain (search for similar items in EconPapers)
JEL-codes: C12 C14 C52 (search for similar items in EconPapers)
Pages: 73
Date: 2020-03-12
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