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. Copyright © 2015 John Wiley & Sons, Ltd.