Testing Dependence among Serially Correlated Multi-Category Variables

The contingency table literature on tests for dependence among discrete multi-category variables is extensive. Existing tests assume, however, that draws are independent, and there are no tests that account for serial dependencies - a problem that is particularly important in economics and finance. This paper proposes a new test of independence based on the maximum canonical correlation between pairs of discrete variables. We also propose a trace canonical correlation test using dynamically augmented reduced rank regressions or an iterated weighting method in order to account for serial dependence. Such tests are useful, for example, when testing for predictability of one sequence of discrete random variables by means of another sequence of discrete random variables as in tests of market timing skills or business cycle analysis. The proposed tests allow for an arbitrary number of categories, are robust in the presence of serial dependencies and are simple to implement using multivariate regression methods. Monte Carlo experiments show that the proposed tests have good finite sample properties. An empirical application to survey data on forecasts of GDP growth demonstrates the importance of correcting for serial dependencies in predictability tests.