Philippine Journal of Science
151 (2): 563-574, April 2022
ISSN 0031 – 7683
Date Received: 08 Nov 2021

Estimation of Poisson Autoregressive Model
for Multiple Time Series

Paolo Victor T. Redondo, Joseph Ryan G. Lansangan, and Erniel B. Barrios*

School of Statistics, University of the Philippines Diliman
Quezon City 1101 Philippines

*Corresponding author: ebbarrios@up.edu.ph

 

[Download]
Redondo PV et al. 2022. Estimation of Poisson Autoregressive Model for Multiple
Time Series. Philipp J Sci 151(2): 563–574. https://doi.org/10.56899/151.02.02

 

ABSTRACT

A Poisson autoregressive (PAR) model accounting for discreteness and autocorrelation of count time series data is typically estimated in the state-space modeling framework through an extended Kalman filter. However, because of the complex dependencies in count time series, estimation becomes more challenging. PAR is viewed as an additive model and estimated using a hybrid of cubic smoothing splines and maximum likelihood estimation (MLE) in the backfitting framework. Simulation studies show that this estimation method is at the least comparable to PAR estimated in the state-space context, especially with larger counts. The flexibility of the additive model has two significant benefits: [1] robust estimation in the presence of temporary structural change and [2] viability to integrate the PAR model into a more complex model structure. We further generalized the PAR(p) model into multiple time series of counts and illustrated it with indicators in the financial markets.