Testing Dependence Among Serially Correlated Multicategory Variables

Abstract

The contingency table literature on tests for dependence among discrete multicategory variables is extensive. Standard tests assume, however, that draws are independent and only limited results exist on the effect of serial dependency—a problem that is important in areas such as economics, finance, medical trials, and meteorology. This article proposes new tests of independence based on canonical correlations from dynamically augmented reduced rank regressions. The tests allow for an arbitrary number of categories as well as multiway tables of arbitrary dimension and are robust in the presence of serial dependencies that take the form of finite-order Markov processes. 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 finite sample properties. An empirical application to microeconomic survey data on firms' forecasts of changes to their production and prices demonstrates the importance of correcting for serial dependencies in predictability tests.