Testing Dependence Among Serially Correlated Multicategory Variables

The contingency table literature on tests for dependence among discrete multi-category variables is extensive. Standard tests assume, however, that draws are independent and only limited results exist on the e¤ect of serial dependency a problem that is important in areas such as economics, …nance, medical trials and meteorology. This paper proposes new tests of independence based on canonical correlations between discretely observed variables. The average canonical correlation statistic is shown to be the same as the familiar Pearson 2 statistic in the case of two-way contingency tables. Dynamically augmented versions of the tests are then proposed that allow for general serial dependencies and do not require the underlying processes to be reversible Markovian processes as assumed by Tavare (1983). The proposed tests allow for an arbitrary number of categories as well as multi-way tables of arbitrary dimension, are robust in the presence of serial dependencies and are simple to implement using multivariate regression methods. For three-way or higher order tables we propose new tests of joint and marginal independence. Monte Carlo experiments show that the proposed tests have good …nite sample properties. An empirical application to survey data on forecasts of GDP growth demonstrates the importance of correcting for serial dependencies in predictability tests.