Copula-Based Vector Autoregressive Models for Bivariate Cointegrated Data

Year: 2011       Vol.: 60       No.: 1      

Authors: Hideaki Taima; Ana Maria L. Tabunda,

Abstract:

The copula method is well applied in finance and actuarial science but its application in economic studies is limited and its use in the cointegration framework virtually nil. This paper explores the use of copula method to analyze the remaining dependence after a cointegration relationship is modeled. Specifically, simulated data is used to characterize the behavior of the dependence parameter estimates of several copulas fitted to the distribution of the residuals after cointegrated Vector Autoregressive (VAR) and Vector Error-Correction Mechanism (VECM) models are fitted, as well as evaluate the forecasting ability of the copula-based models. The Clayton, Frank, Gaussian, Gumbel and Plackett copulas are used and are compared on the basis of bias, root mean square error (RMSE) and maximum likelihood. The density forecasting ability of the copula-based VAR and VECM is then compared with that of standard models via conditional Kullback-Leibler Information Criterion (KLIC) divergence measure using simulated and empirical data. The simulation results indicate that the copula-based models generally have better density forecasting ability than standard VAR and VECM models, a finding that is supported in the application of a copula-based VAR to empirical data.

Keywords: Copula; Cointegration; VAR; VECM

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