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

Abstract

<jats:p>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. (<jats:italic>American Journal of Political Science</jats:italic>44(4):823–843, 2000). We develop an alternative model for stationary mean reverting data, the Poisson autoregressive model of order<jats:italic>p</jats:italic>, or PAR(<jats:italic>p</jats:italic>) 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.</jats:p>

Rights to the forest, REDD+ and elections: Mining in Guyana

“…This creates problems with the use of possible estimation techniques for TSCS data such as Ordinary Least Squares (OLS) with PanelCorrected Standard Errors (Beck & Katz, 1996). One alternative approach that could counter the non-normality would be the use of a negative binomial or Poisson models however such models prove difficult to incorporate dynamic elements, crucial for analysing time-series data (Brandt, Williams, Fordham, &Pollins, 2000 andWilliams 2001). 25 These techniques are suitable for independent, identically distributed data, but are problematic when there is dependence over time,…”

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“…If errors are Gaussian, then the usual time series modelling technique can be applied. If not, then there is need to write down conditional density function to proceed with identification and estimation (Brandt and Williams 2001).…”

A Bayesian Poisson Vector Autoregression Model

“…This is particularly the case if there are observed zero counts in the data. Brandt et al (2000) and Brandt and Williams (2001) extend the Poisson regression estimator to allow for dynamic processes. They present Monte Carlo results that demonstrate that when counts are serially correlated, the use of dynamic Poisson regression models produces less biased and more efficient estimates than a standard Poisson regression estimator.…”

“…For dynamic event count data, such an assumption is not tenable and produces biased estimates (per the findings in King (1988) and Brandt and Williams (2001)). So while these methods will work for count series that are approximately normal, they may fail when applied to the dynamic events like those that we are interested in here.…”

“…Despite counts of many phenomena, the bulk of the count models, employed in political science, are univariate. These univariate count models have been extended to allow for various dynamic count processes from moving averages, to autoregressions, to changepoints (Brandt et al, 2000;Brandt and Williams, 2001;Park, 2010).…”