A new First-Order mixture integer-valued threshold autoregressive process based on binomial thinning and negative binomial thinning

TL;DR

This paper introduces a novel first-order mixture integer-valued threshold autoregressive model utilizing binomial and negative binomial thinning, with statistical properties, estimation methods, and real-world application demonstrated.

Contribution

The paper presents a new threshold autoregressive model based on thinning operators, along with its statistical properties, estimation techniques, and an application to crime data.

Findings

Model effectively captures count data with threshold behavior

Estimation methods show good asymptotic properties

Application to Pittsburgh crime data demonstrates practical utility

Abstract

In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the asymptotic properties of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset.