A new geometric INAR(1) process based on counting series with deflation or inflation of zeros. Issue 17 (22nd November 2018)

• Record Type: Journal Article
• Authors: Bourguignon, Marcelo; Borges, Patrick; Fajardo Molinares, Fabio
• Is Part Of: Journal of statistical computation and simulation. Volume 88:Issue 17(2018)
• Page Start: 3338
• Page End: 3348
• Publication Date: 2018-11-22
• Subjects: Integer-valued time series -- overdispersion -- zero-modified geometric distribution; 62M05 -- 62M10; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2018.1516220
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: In this paper, we introduce a new non-negative integer-valued autoregressive time series model based on a new thinning operator, so called generalized zero-modified geometric (GZMG) thinning operator. The first part of the paper is devoted to the distribution, GZMG distribution, which is obtained as the convolution of the zero-modified geometric (ZMG) distributed random variables. Some properties of this distribution are derived. Then, we construct a thinning operator based on the counting processes with ZMG distribution. Finally, an INAR(1) time series model is introduced and its properties including estimation issues are derived and discussed. A small Monte Carlo experiment is conducted to evaluate the performance of maximum likelihood estimators in finite samples. At the end of the paper, we consider an empirical illustration of the introduced INAR(1) model.