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<p>This paper focuses on modeling time series of counts using an integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) framework. The used approach involves modeling the marginal components of the time series using the exponential family INGARCH approach, while allowing the conditional mean to be recursively generated from all components. Moreover, akin to the classical GARCH framework, the proposed multiplicative INGARCH (mINGARCH) model is constructed as the product of a latent INGARCH process and an iid error process to account for random effects. This formulation is further extended to a multivariate version (mMINGARCH). Parameter estimation methods are also presented, including the use of the exponential family quasi-likelihood estimator and the weighted least squares estimator. The proposed methodologies are validated through Monte Carlo simulations and a real data analysis, where monthly crime count data from New South Wales, Australia, is analyzed.</p>

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Inference for multivariate time series of counts via multiplicative INGARCH modeling

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • Sangyeol Lee,
  • Byungsoo Kim,
  • Minyoung Jo

摘要

This paper focuses on modeling time series of counts using an integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) framework. The used approach involves modeling the marginal components of the time series using the exponential family INGARCH approach, while allowing the conditional mean to be recursively generated from all components. Moreover, akin to the classical GARCH framework, the proposed multiplicative INGARCH (mINGARCH) model is constructed as the product of a latent INGARCH process and an iid error process to account for random effects. This formulation is further extended to a multivariate version (mMINGARCH). Parameter estimation methods are also presented, including the use of the exponential family quasi-likelihood estimator and the weighted least squares estimator. The proposed methodologies are validated through Monte Carlo simulations and a real data analysis, where monthly crime count data from New South Wales, Australia, is analyzed.