A new minification integer‐valued autoregressive process driven by explanatory variables. (28th December 2022)

• Record Type: Journal Article
• Authors: Qian, Lianyong; Zhu, Fukang
• Is Part Of: Australian & New Zealand journal of statistics. Volume 64:Number 4(2022)
• Page Start: 478
• Page End: 494
• Publication Date: 2022-12-28
• Subjects: autoregression -- explanatory variables -- minification process -- time series of counts; Statistics -- Periodicals; 519.5
• DOI: 10.1111/anzs.12379
• Languages: English
• ISSNs: 1369-1473

Abstract

Summary: The discrete minification model based on the modified negative binomial operator, as an extension to the continuous minification model, can be used to describe an extreme value after few increasing values. To make this model more practical and flexible, a new minification integer‐valued autoregressive process driven by explanatory variables is proposed. Ergodicity of the new process is discussed. The estimators of the unknown parameters are obtained via the conditional least squares and conditional maximum likelihood methods, and the asymptotic properties are also established. A testing procedure for checking existence of the explanatory variables is developed. Some Monte Carlo simulations are given to illustrate the finite‐sample performances of the estimators under specification and misspecification and the test, respectively. A real example is applied to illustrate the performance of our model.