Time Series of Zero‐Inflated Counts and their Coherent Forecasting

Abstract

Poisson integer-valued auto-regressive process of order 1 (PINAR(1)) due to Al-Osh and Alzaid (Journal of Time Series Analysis 1987; 8(3): 261-275) and McKenzie (Advances in Applied Probability 1988; 20(4): 822-835) has received a significant attention in modelling low-count time series during the last two decades because of its simplicity. But in many practical scenarios, the process appears to be inadequate, especially when data are overdispersed in nature. This overdispersion occurs mainly for three reasons: presence of some extreme values, large number of zeros, and presence of both extreme values with a large number of zeros. In this article, we develop a zero-inflated Poisson INAR(1) process as an alternative to the PINAR(1) process when the number of zeros in the data is larger than the expected number of zeros by the Poisson process. We investigate some important properties such as stationarity, ergodicity, autocorrelation structure, and conditional distribution, with a detailed study on h-step-ahead coherent forecasting. A comparative study among different methods of parameter estimation is carried out using some simulated data. One real dataset is analysed for practical illustration.

Testing the constancy of the thinning parameter in a random coefficient integer autoregressive model

“…The application areas of these types of integer-valued time series include epidemiology, actuarial statistics, neurobiology, psychometry etc. See for example Ristić et al (2009), Moriña et al (2011), Park and Kim (2012), Maiti et al (2015) and Davis et al (2016) .…”

The need for location-specific biometeorological indexes in Taiwan

“…EAS demand was selected because it is generally of higher volume than hospitalization and mortality. This could prevent the need to deal with low count time series data and would make the relationship between weather and EAS demand easier to examine than those of hospitalization and mortality rates ( 19 , 20 ). A full understanding of the relationship between EAS demand and biometeorological indexes will help the Central Weather Bureau to forewarn the public about the impact of coming adverse weather in a more effective way.…”

Change‐point analysis through integer‐valued autoregressive process with application to some COVID‐19 data

“…For example, McKenzie (1985McKenzie ( , 1986 and Al-Osh and Alzaid (1987) introduced a class of stationary integer-valued autoregressive (INAR) time series process based on binomial thinning operator. This process was further studied and generalized by Alzaid and Al-Osh (1990), Jin-Guan and Yuan (1991), Freeland and McCabe (2004), Risti ć, Bakouch, and Nasti ć (2009), Jazi, Jones, and Lai (2012), Schweer and Weiß, (2014), Maiti, Biswas, and Das (2015) and many more.…”

“…Risti ć et al (2009) and Schweer and Weiß (2014) proposed a new INAR(1) process based on negative binomial thinning operator which can also handle the overdispersion problem. Jazi et al (2012) and Maiti et al (2015) studied zero-inflated PINAR(1) (ZIPINAR(1)) processes for zero-inflated count data. Apart from these thinning-based INAR processes, Cameron and Trivedi (1986) and Fokianos (2011) studied some regression-based time series models to model count time series data.…”