Goodness-of-Fit Test for Specification of Copula-Based Semiparametric Time-Series Models

• Activity Number: 235
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Qian Zhou*+ and Shulin Zhang and Huazhen Lin
• Companies: Simon Fraser University and Southwestern University of Finance and Economics, China and Southwestern University of Finance and Economics, China
• Keywords: in-and-out sample conditional pseduo-likelihood ; model misspecifiction ; semiparametric copulas ; time-series

Abstract

Recently, copulas have become increasingly popular in modelling the temporal dependence of a univariate nonlinear time series since they allow one to model and estimate the marginal distribution and dependence structure separately. Semi-parametric copula models are characterized by unspecified marginal distributions and parametric copula functions. Misspecification on parametric structures of copula functions may cause misleading statistical estimation and inference. In this talk, we propose a new test constructed via the contrast between "in-sample" and "out-of-sample" conditional pseudo-likelihoods. Under the null hypothesis that the copula model is correctly specified, we show that the proposed test statistic converges in probability to a constant equal to the dimension of the parameter space and establish the asymptotic normality for the test.