Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression

Abstract

In this paper, we present a novel family of multivariate mixed Poisson-Generalized Inverse Gaussian INAR(1), MMPGIG-INAR(1), regression models for modelling time series of overdispersed count response variables in a versatile manner. The statistical properties associated with the proposed family of models are discussed and we derive the joint distribution of innovations across all the sequences. Finally, for illustrative purposes different members of the MMPGIG-INAR(1) class are fitted to Local Government Property Insurance Fund data from the state of Wisconsin via maximum likelihood estimation.

A multivariate heavy-tailed integer-valued GARCH process with EM algorithm-based inference

“…Very limited research is available to address the problem of modeling multivariate count time series that exhibit heavytailed behavior. Such a feature is commonly seen in many real-data situations such as numbers of insurance claims for different types of properties (Chen et al 2023), and highfrequency trading volume in the financial market (Qian et al 2020), to name a few.…”

“…(v) Our modeling approach involves a latent random variable whose parameters relate to contemporaneous correlation. A related work to ours is Chen et al (2023), where a first-order multivariate count model based on the INAR approach with innovations following a multivariate Poisson generalized inverse-Gaussian distribution is introduced. The estimation of parameters of their model is performed via the method of maximum likelihood.…”

“…Besides this model not having a computationally feasible estimation technique, especially for higher dimensions, it does not handle all the features of our model mentioned in (i) above, for instance, allowing for negative autocorrelations. Moreover, the parameter related to the tail is fixed by Chen et al (2023) in their model to some values that correspond to certain known/explicit distributions. In our case, we assume that such a parameter is unknown and show that it can be efficiently estimated.…”