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Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model

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  • Heinen, Andreas

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 time-varying. 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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8113.

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Date of creation: Jul 2003
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Handle: RePEc:pra:mprapa:8113

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Keywords: Forecast; volatility; transactions data;

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References

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  1. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," NBER Technical Working Papers 0215, National Bureau of Economic Research, Inc.
  2. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422, October.
  3. Gurmu, Shiferaw & Trivedi, Pravin K., 1993. "Variable Augmentation Specification Tests in the Exponential Family," Econometric Theory, Cambridge University Press, vol. 9(01), pages 94-113, January.
  4. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  5. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-17, October.
  6. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. Lee, Charles M C & Ready, Mark J, 1991. " Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-46, June.
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