A Periodic Conditional Poisson Model

• Activity Number: 519 - SPEED: Methodological Advances in Time Series: BandE Speed Session, Part 2
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 11:15 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yi Zhang* and V A Samaranayake
• Companies: Missouri Univeristy of Science and Technology and Missouri University of Science and Technology
• Keywords: count data; seasonality; discrete time series; conditional heteroscedasticity

Abstract

A periodic version of the autoregressive conditional Poisson model (ACP), introduced by Heinen [1] in 2003 , is proposed. In the ACP model, the conditional mean of the Poisson process at a given time is assumed to follow a formulation that links it to past counts and past means. The proposed Periodic Autoregressive Conditional Poisson (PACP) model assumes that the data are generated by Poisson process whose conditional mean follows an ACP model with parameters that varies seasonally. Such models would be more appropriate when modeling count data series exhibiting conditional heteroskedastic behavior that varies from season to season. Properties of the model are investigated, and an alternative format of the model is presented to make it comparable to a vector ARMA process. A Monte Carlo simulation study, that employs the maximum likelihood method to estimate the parameters, shows an accurate estimation of the parameters with a relatively small Monte Carlo standard error. The simulation study also investigated the use of AIC and BIC criteria to differentiate between periodic and non-periodic cases with promising results. An analysis of a simulated data is used to illustrate the importance of identifying the true structure of time series count data with periodic behavior and potential for the wide uses of such models