Dynamic Orthogonal Components for Multivariate Time Series

We introduce dynamic orthogonal components (DOC) for multivariate time series and propose a procedure for estimating and testing the existence of DOCs for a given time series. We estimate the dynamic orthogonal components via a generalized decorrelation method that minimizes the linear and quadratic dependence across components and across time. We then use Ljung-Box type statistics to test the existence of dynamic orthogonal components. When DOCs exist, univariate analysis can be applied to build a model for each component. Those univariate models are then combined to obtain a multivariate model for the original time series. We demonstrate the usefulness of dynamic orthogonal components with two real examples and compare the proposed modeling method with other dimension-reduction methods available in the literature, including principal component and independent component analyses. We also prove consistency and asymptotic normality of the proposed estimator under some regularity conditions. We provide some technical details in online Supplementary Materials.