Zero-inflated Poisson Integer Valued GARCH Model with Periodic Coefficients

Accepted - October 2024

Abstract

In this paper we introduce the zero-inflated Poisson integer-valued generalized autoregressive conditional heteroskedastic model with periodic coefficients, to address two critical aspects: the zeroinflated nature of count time series and the presence of periodic features hidden in the autocorrelation function. The study focuses on analyzing the fundamental probabilistic and statistical
properties of this class. Specifically, the conditions for the existence of higher order moments are
obtained and their explicit formulas in terms of the model parameters are derived. In particular,
the periodic stationarity conditions for the first and second moments are established, and their
closed-form expressions are derived based on the obtained conditions. Furthermore, the research
examines the periodic autocovariance structure and provides a closed-form expression for the periodic
autocorrelation function. To estimate the underlying parameters, the Conditional Maximum
Likelihood (CML) method is applied, using the Expectation Maximization (EM) algorithm. The
effectiveness of this method is assessed through a simulation study. Additionally, the paper illustrates
the practical application of the proposed model by analyzing the daily number of COVID-19
deaths in Finland.