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<p>This work addresses the modeling of multiple related time series with non-negative observations, many of which contain non-negligible portions of zeros. Each series is modeled univariately as a GARCH process, constrained to non-negative values. A parametric copula is used to introduce dependence among the time series, with the occurrence of zeros assumed to follow a multivariate Markov chain. The goal is to estimate the omnibus model parameters. The multivariate hurdle distribution and the dependence of zeros cause classical estimation techniques to fail. Therefore, a partial quasi-maximum likelihood approach is employed, using a generalized density supported on the closed orthant. Under simple and easily verifiable assumptions, the estimated parameters of the joint model are shown to be consistent. The empirical properties are demonstrated in a simulation study.</p>

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Copula hurdle GARCH models for multivariate non-negative time series

  • 期刊论文

  • 发表日期：

    2025年5月6日

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  • Šárka Hudecová,
  • Michal Pešta

摘要

This work addresses the modeling of multiple related time series with non-negative observations, many of which contain non-negligible portions of zeros. Each series is modeled univariately as a GARCH process, constrained to non-negative values. A parametric copula is used to introduce dependence among the time series, with the occurrence of zeros assumed to follow a multivariate Markov chain. The goal is to estimate the omnibus model parameters. The multivariate hurdle distribution and the dependence of zeros cause classical estimation techniques to fail. Therefore, a partial quasi-maximum likelihood approach is employed, using a generalized density supported on the closed orthant. Under simple and easily verifiable assumptions, the estimated parameters of the joint model are shown to be consistent. The empirical properties are demonstrated in a simulation study.