On canonical analysis of multivariate time series

Canonical correlation analysis has been widely used in the literature to identify the underlying structure of a multivariate linear time series. Most of the studies assume that the innovations to the multivariate system are Gaussian. On the other hand, there are many applications in which the normality assumption is either questionable or clearly inadequate. For example, most empirical time series in business and finance exhibit conditional heteroscedasticity and have high excess kurtosis. In this paper, we establish some asymptotic results for canonical correlation analysis of multivariate linear time series when the data possess conditional heteroscedasticity. We show that for correct identification of a multivariate time series model, it is essential to use a modification, which we prescribe, to a commonly used test statistic for testing zero canonical correlations. We also use simulation to study the efficacy of the modification, and apply the modified test statistics to analyze daily log returns of three assets.