A0638
Title: Statistical methods for multivariate time series with arbitrary distributions
Authors: Bruno Remillard - HEC Montreal (Canada) [presenting]
Bouchra Nasri - University of Montreal (Canada)
Kilani Ghoudi - United Arab Emirates University (United Arab Emirates)
Abstract: Generalized innovations are defined and associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility models and regime-switching models with possibly zero-inflated regimes. The main novelty of this article is it is able to test for conditional independence between several time series with arbitrary distributions, extending previous study results obtained only for stochastic volatility models. Families of empirical processes are defined and constructed from lagged generalized errors, and it is shown that their joint asymptotic distributions are Gaussian and independent of the estimated parameters of the individual time series. Mobius transformations of the empirical processes are used to obtain tractable covariances. Several test statistics are then proposed based on Cramer von Mises-type statistics and dependence measures, as well as graphical methods to visualize the dependence. In addition, numerical experiments are performed to assess the power of the proposed tests. Finally, to show the usefulness of methodologies, examples of applications for financial data and crime data are given to cover both discrete and continuous cases. All developed methodologies are implemented in the CRAN package IndGenErrors.
