Leitura do dia - autoregressive poisson process

Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model

Andreas Heinen

This paper introduces and evaluates new models for time series count data. The
Autoregressive Conditional Poisson model (ACP) makes it possible to deal with issues
of discreteness, overdispersion (variance greater than the mean) and serial correlation.
A fully parametric approach is taken and a marginal distribution for the counts is spec-
ified, where conditional on past observations the mean is autoregressive. This enables
to attain improved inference on coefficients of exogenous regressors relative to static
Poisson regression, which is the main concern of the existing literature, while mod-
elling the serial correlation in a flexible way. A variety of models, based on the double
Poisson distribution of Efron (1986) is introduced, which in a first step introduce an
additional dispersion parameter and in a second step make this dispersion parameter
time-varying. All models are estimated using maximum likelihood which makes the
usual tests available. In this framework autocorrelation can be tested with a straight-
forward likelihood ratio test, whose simplicity is in sharp contrast with test procedures
in the latent variable time series count model of Zeger (1988). The models are applied
to the time series of monthly polio cases in the U.S between 1970 and 1983 as well
as to the daily number of price change durations of :75$ on the IBM stock. A :75$
price-change duration is de¯ned as the time it takes the stock price to move by at least
:75$. The variable of interest is the daily number of such durations, which is a measure
of intradaily volatility, since the more volatile the stock price is within a day, the larger
the counts will be. The ACP models provide good density forecasts of this measure of
volatility.