Goodness-of- fit tests for multivariate copula-based time series models
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Date
2014-05-21
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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.
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Keywords
empirical process, semiparametric copula model, ranks, pseudo-observations, multivariate observations, Markov chain, multiplier central limit theorem