Estimation of Poisson Autoregressive Model for Multiple Time Series

TL;DR

This paper introduces a novel estimation method for Poisson autoregressive models using cubic smoothing splines and MLE, demonstrating improved performance over traditional state-space approaches, especially for larger counts and nonstationary data.

Contribution

It proposes a hybrid estimation approach for PAR models that enhances robustness and flexibility, and extends the model to multiple time series with financial market applications.

Findings

Estimation method performs better than state-space approaches for larger counts.

Method shows robustness to structural changes in data.

Extended model successfully applied to financial market indicators.

Abstract

A Poisson autoregressive (PAR) model accounting for discreteness and autocorrelation of count time series data is typically estimated in the state-space modelling framework through 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 comparable or better than PAR estimated in the state-space context, especially with larger count values. However, as [2] formulated PAR for stationary counts, both estimation procedures underestimate parameters in nearly nonstationary models. The flexibility of the additive model has two benefits though: robust estimation in the presence of temporary structural change, and; viability to integrate PAR model into a more complex model structure. We further generalized the PAR(p) model into multiple time series of counts and illustrated with indicators in the financial markets.