Analysis of Count Time Series Through Integer‐Valued Autoregressive (INAR) Process With Zero‐Inflation and Seasonality

Abstract

In this article, we study a count time‐series data of weekly dengue cases in Kaohsiung City, Taiwan during the period 2009–2012, where the problems of a large number of zeros or zero‐inflation and seasonality arise together. To capture both features, we consider an application‐oriented zero‐inflated seasonal PINAR framework based on zero‐inflated Poisson innovations. We also incorporate an exogenous variable, namely the weekly maximum temperature, in the innovations to study the effect of temperature on the number of dengue cases as many studies have found that temperature is a significant factor in spreading dengue infections globally. The proposed model can capture both the non‐recovery cases from the previous time point and the new cases coming at the current time point. The distributional and forecasting properties of the proposed model are derived. The consistency and asymptotic normality of the CLS estimator are established under suitable regularity conditions, and simulation experiments are used to examine the finite‐sample estimation and forecasting performance of the proposed model. The proposed model is compared with some existing INAR models. Finally, we analyze the data of weekly dengue cases in Kaohsiung for practical illustration.