Goodness-of- fit tests for multivariate copula-based time series models

Abstract

In recent years, stationary time series models based on copula functions became increasingly popular in econometrics to model nonlinear temporal and cross-sectional dependencies. Within these models, we consider the problem of testing the goodness-of-fit of the parametric form of the underlying copula. Our approach is based on a dependent multiplier bootstrap and it can be applied to any stationary, strongly mixing time series. The method extends recent i.i.d. results by Kojadinovic, Yan and Holmes [I. Kojadinovic, Y. Yan and M. Holmes, Fast large sample goodness-of- fit tests for copulas, Statistica Sinica 21 (2011), 841{871] and shares the same computational benefits compared to methods based on a parametric bootstrap. The finite-sample performance of our approach is investigated by Monte Carlo experiments for the case of copula-based Markovian time series models.