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Serial Correlation in Contingency Tables (Helmut Elsinger)

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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.

Suggested Citation

  • Helmut Elsinger, 2020. "Serial Correlation in Contingency Tables (Helmut Elsinger)," Working Papers 228, Oesterreichische Nationalbank (Austrian Central Bank).
    • Handle: RePEc:onb:oenbwp:228
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    References listed on IDEAS

    as
    1. Chou, Cheng & Chu, Chia-Shang J., 2010. "Testing independence of two autocorrelated binary time series," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 69-75, January.
    2. Pesaran, M. Hashem & Timmermann, Allan, 2009. "Testing Dependence Among Serially Correlated Multicategory Variables," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 325-337.
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    More about this item

    Keywords

    Goodness of Fit; Independence Tests; Cochrane-Mantel-Haenszel Test; Markov chain;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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