Tests for independence in a bivariate negative binomial model

Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression

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 bivariate INAR(1) process with application

The study of time series models for count data has become a topic of special interest during the last years. However, while research on univariate time series for counts now flourishes, the literature on multivariate time series models for count data is notably more limited. In the present paper, a bivariate integer-valued autoregressive process of order 1 (BINAR(1)) is introduced. Emphasis is placed on models with bivariate Poisson and bivariate negative binomial innovations. We discuss properties of the BINAR(1) model and propose the method of conditional maximum likelihood for the estimation of its unknown parameters. Issues of diagnostics and forecasting are considered and predictions are produced by means of the conditional forecast distribution. Estimation uncertainty is accommodated by taking advantage of the asymptotic normality of maximum likelihood estimators and constructing appropriate confidence intervals for the fe-step-ahead conditional probability mass function. The proposed model is applied to a bivariate data series concerning daytime and nighttime road accidents in the Netherlands.