Heinen, Andreas (2003): Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model.

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Abstract
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 specified, 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 modelling 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 timevarying. All models are estimated using maximum likelihood which makes the usual tests available. In this framework autocorrelation can be tested with a straightforward 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 defined 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.
Item Type:  MPRA Paper 

Original Title:  Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model 
Language:  English 
Keywords:  Forecast; volatility; transactions data 
Subjects:  G  Financial Economics > G1  General Financial Markets C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C53  Forecasting and Prediction Methods; Simulation Methods C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C25  Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions 
Item ID:  8113 
Depositing User:  Heinen 
Date Deposited:  07. Apr 2008 00:28 
Last Modified:  11. Feb 2013 21:15 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/8113 