A Linear Poisson Autoregressive Model: The Poisson AR(p) Model

Time series of event counts are common in political science and other social science applications. Presently, there are few satisfactory methods for identifying the dynamics in such data and accounting for the dynamic processes in event counts regression. We address this issue by building on earlier work for persistent event counts in the Poisson exponentially weighted moving-average model (PEWMA) of Brandt et al. (American Journal of Political Science 44(4):823–843, 2000). We develop an alternative model for stationary mean reverting data, the Poisson autoregressive model of order p, or PAR(p) model. Issues of identification and model selection are also considered. We then evaluate the properties of this model and present both Monte Carlo evidence and applications to illustrate.