Mathematics

Categorical variable

Poisson distribution

Statistics

Autoregressive model

Econometrics

Negative binomial distribution

Ergodicity

Covariance

Conditional variance

Autoregressive conditional heteroskedasticity

Applied mathematics

Quasi-likelihood

Volatility (finance)

Communication in Statistics- Theory and Methods

In this paper, two-parameter Poisson binomial-exponential 2 (PBE2) distribution is firstly reviewed, then a new integer-valued autoregressive (INAR) model with PBE2 innovations is proposed. The definition and statistical properties of the proposed model are given, including the mean, variance, covariance, strict stationarity and ergodicity. Two-step conditional least squares and conditional maximum likelihood estimation methods are considered to estimate the parameters. To assess the proposed model, a crime data set is analyzed and a comparison with other competing INAR models is given, which shows that the proposed model yields a better performance.

A new INAR model based on Poisson-BE2 innovations