Modeling Dependence in Vector Stochastic Processes

• Activity Number: 214
• Type: Topic Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economics Statistics Section
• Author(s): Paul Dagum*+
• Companies: Rapt, Inc.
• Keywords: non-normal ; stochastic process ; copula ; nonlinear

Abstract

The dependencies in a vector stochastic process arise from temporal dependencies within processes and dependencies across processes. Both sets of dependencies may express nonlinear switching behavior that is regime-dependent. Joint models for these processes typically invoke assumptions about linearity or normality of distributions. Among these are Brownian motion models that are instances of a Gaussian process. We propose a copula approach for separately modeling the marginal distributions and dependencies of vector stochastic processes. We allow for separate copulas to model the contemporaneous dependencies and the temporal dependencies including finite mixture copulas with categorical variables that permit model switching. By decoupling the specification of the marginal distribution from the dependence model, inferences on dependencies are robust to the specification of the marginal distribution. The approach admits nonnormal and nonparametric marginal distributions. We discuss economic and business applications.