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Zero‐Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros
Author(s) -
BarretoSouza Wagner
Publication year - 2015
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12131
Subject(s) - mathematics , overdispersion , autoregressive model , estimator , deflation , count data , series (stratigraphy) , geometric series , inflation (cosmology) , zero (linguistics) , econometrics , statistics , mathematical analysis , monetary policy , poisson distribution , paleontology , linguistics , physics , philosophy , theoretical physics , monetary economics , economics , biology , power series
In this article, we propose a first‐order integer‐valued autoregressive [INAR(1)] process for dealing with count time series with deflation or inflation of zeros. The proposed process has zero‐modified geometric marginals and contains the geometric INAR(1) process as a particular case. The proposed model is also capable of capturing underdispersion and overdispersion, which sometimes are caused by deflation or inflation of zeros. We explore several statistical and mathematical properties of the process, discuss point estimation of the parameters and find the asymptotic distribution of the proposed estimators. We also propose a test based on our model for checking if the count time series considered is deflated or inflated of zeros. Two empirical illustrations are presented in order to show the potential for practice of our zero‐modified geometric INAR(1) process. This article contains a Supporting Information.