Statistics and Its Interface

Volume 11 (2018)

Number 4

Modelling time series of counts with deflation or inflation of zeros

Pages: 631 – 639



Marcelo Bourguignon (Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil)


In this paper, we introduce a first order non-negative integer valued autoregressive process with zero-modified geometric innovations based on the binomial thinning operator. This new model will enable one to tackle the problem of deflation or inflation of zeros inherent in the analysis of integer-valued time series data, and contains the INARG(1) model as a particular case. The main properties of the model are derived, such as mean, variance, autocorrelation function, transition probabilities and zero probability. The methods of conditional maximum likelihood, Yule–Walker and conditional least squares are used for estimating the model parameters. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. The proposed model is fitted to time series of emergency counts department of a children’s hospital and of drugs reselling criminal acts counts illustrating its capabilities in challenging cases of deflated and inflated count data.


estimation, INAR(1) process, Integer-valued time series, zero-modified geometric distribution

2010 Mathematics Subject Classification


Received 22 June 2017

Published 19 September 2018