Long Run Canonical Correlations : Estimation and Inference

This paper proposes methods for both the consistent estimation of so-called long run canonical correlations (LRCCs) and also testing the null hypothesis that a subset of LRCCs are zero. Two test statistics are proposed and their limiting distribution is derived under the null hypothesis. It is shown that the statistics provide a natural way for testing the asymptotic independence of two standardized sums. The tests are illustrated via an application to a cointegration model in which it is shown that inference is only tractable if a certain LRCC is zero