A new test for the proportionality of two large-dimensional covariance matrices

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Robust Unit Root and Cointegration Rank Tests for Panels and Large Systems

This study develops new tests for unit roots and cointegration rank in heterogeneous time series panels using methods that are robust to the presence of both incidental trends and cross sectional dependency of unknown form. Furthermore, the procedures do not require a choice of lag truncation or bandwidth to accommodate higher order serial correlation. The cointegration rank tests can also be implemented in relatively large dimensioned systems of equations for which conventional VECM based tests become infeasible. Monte Carlo simulations demonstrate that the procedures have high power and good size properties even in panels with relatively small dimensions.Panel Unit Roots, Cointegration Rank Tests, Robust Autocovariance Estimation

Testing for patterns and structures in covariance and correlation matrices

Covariance matrices of random vectors contain information that is crucial for modelling. Certain structures and patterns of the covariances (or correlations) may be used to justify parametric models, e.g., autoregressive models. Until now, there have been only few approaches for testing such covariance structures systematically and in a unified way. In the present paper, we propose such a unified testing procedure, and we will exemplify the approach with a large variety of covariance structure models. This includes common structures such as diagonal matrices, Toeplitz matrices, and compound symmetry but also the more involved autoregressive matrices. We propose hypothesis tests for these structures, and we use bootstrap techniques for better small-sample approximation. The structures of the proposed tests invite for adaptations to other covariance patterns by choosing the hypothesis matrix appropriately. We prove their correctness for large sample sizes. The proposed methods require only weak assumptions. With the help of a simulation study, we assess the small sample properties of the tests. We also analyze a real data set to illustrate the application of the procedure