EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects

Zezhun Chen*, Angelos Dassios, George Tzougas

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
27 Downloads (Pure)

Abstract

This article considers bivariate mixed Poisson INAR(1) regression models with correlated random effects for modelling correlations of different signs and magnitude among time series of different types of claim counts. This is the first time that the proposed family of INAR(1) models is used in a statistical or actuarial context. For expository purposes, the bivariate mixed Poisson INAR(1) claim count regression models with correlated Lognormal and Gamma random effects paired via a Gaussian copula are presented as competitive alternatives to the classical bivariate Negative Binomial INAR(1) claim count regression model which only allows for positive dependence between the time series of claim count responses. Our main achievement is that we develop novel alternative Expectation-Maximization type algorithms for maximum likelihood estimation of the parameters of the models which are demonstrated to perform satisfactory when the models are fitted to Local Government Property Insurance Fund data from the state of Wisconsin.

Original languageEnglish
Pages (from-to)225-255
Number of pages31
JournalEuropean Actuarial Journal
Volume14
Issue number1
Early online date6 Jun 2023
DOIs
Publication statusPublished - Apr 2024

Keywords

  • Binomial-mixed Poisson INAR(1) regression models with correlated random effects
  • Correlations of different signs and magnitude
  • Count data time series
  • Gaussian copula
  • Overdispersion

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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