A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.

Automated summary

In this paper, a new integer-valued autoregressive model is introduced based on the extended binomial thinning operator, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares estimation and conditional maximum likelihood estimation methods are proposed for the model. Moreover, the asymptotic property of the two-step conditional least squares estimator is also obtained, and the proposed model is demonstrated to have superior performance through the analysis of real data sets with different dispersion levels.