Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model
AbstractThis 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 InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 8113.
Date of creation: Jul 2003
Date of revision:
Forecast; volatility; transactions data;
Other versions of this item:
- HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," CORE Discussion Papers 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- G1 - Financial Economics - - General Financial Markets
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
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- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997.
"Evaluating density forecasts,"
97-6, Federal Reserve Bank of Philadelphia.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," Center for Financial Institutions Working Papers 97-37, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," NBER Technical Working Papers 0215, National Bureau of Economic Research, Inc.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, . "Evaluating Density Forecasts," CARESS Working Papres 97-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- 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.
- 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.
- 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.
- 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.
- 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.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- 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.
- Ralph D. Snyder & Gael M. Martin & Phillip Gould & Paul D. Feigin, 2007. "An Assessment of Alternative State Space Models for Count Time Series," Monash Econometrics and Business Statistics Working Papers 4/07, Monash University, Department of Econometrics and Business Statistics.
- Ralph D. Snyder & Adrian Beaumont, 2007. "A Comparison of Methods for Forecasting Demand for Slow Moving Car Parts," Monash Econometrics and Business Statistics Working Papers 15/07, Monash University, Department of Econometrics and Business Statistics.
- Quoreshi, Shahiduzzaman, 2005. "Modelling High Frequency Financial Count Data," UmeÃ¥ Economic Studies 656, Umeå University, Department of Economics.
- Weiß, Christian H., 2010. "INARCH(1) processes: Higher-order moments and jumps," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1771-1780, December.
- Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004.
"Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks,"
UmeÃ¥ Economic Studies
637, Umeå University, Department of Economics.
- Kurt Brannas & A. M. M. Shahiduzzaman Quoreshi, 2010. "Integer-valued moving average modelling of the number of transactions in stocks," Applied Financial Economics, Taylor and Francis Journals, vol. 20(18), pages 1429-1440.
- Jung, Robert C. & Liesenfeld, Roman & Richard, Jean-FranÃ§ois, 2011.
"Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 29(1), pages 73-85.
- Jung, Robert & Liesenfeld, Roman & Richard, Jean-François, 2008. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Economics Working Papers 2008,12, Christian-Albrechts-University of Kiel, Department of Economics.
- Christian Weiß, 2009. "Modelling time series of counts with overdispersion," Statistical Methods and Applications, Springer, vol. 18(4), pages 507-519, November.
- Ord, J. Keith & Koehler, Anne B. & Snyder, Ralph D. & Hyndman, Rob J., 2009.
"Monitoring processes with changing variances,"
International Journal of Forecasting,
Elsevier, vol. 25(3), pages 518-525, July.
- J. Keith Ord & Rob J. Hyndman & Anne B. Koehler & Ralph D. Snyder, 2008. "Monitoring Processes with Changing Variances," Monash Econometrics and Business Statistics Working Papers 4/08, Monash University, Department of Econometrics and Business Statistics.
- J. Keith Ord, 2008. "Monitoring Processes with Changing Variances," Working Papers 2008-004, The George Washington University, Department of Economics, Research Program on Forecasting.
- Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
- Snyder, Ralph D. & Ord, J. Keith & Beaumont, Adrian, 2012. "Forecasting the intermittent demand for slow-moving inventories: A modelling approach," International Journal of Forecasting, Elsevier, vol. 28(2), pages 485-496.
- Ghahramani, M. & Thavaneswaran, A., 2009. "On some properties of Autoregressive Conditional Poisson (ACP) models," Economics Letters, Elsevier, vol. 105(3), pages 273-275, December.
- Feigin, Paul D. & Gould, Phillip & Martin, Gael M. & Snyder, Ralph D., 2008. "Feasible parameter regions for alternative discrete state space models," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2963-2970, December.
- BEN OMRANE, Walid & HEINEN, Andréas, 2003. "The response of individual FX dealers'quoting activity to macroeconomic news announcements," CORE Discussion Papers 2003070, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Jung, Robert & Kukuk, Martin & Liesenfeld, Roman, 2005. "Time Series of Count Data : Modelling and Estimation," Economics Working Papers 2005,08, Christian-Albrechts-University of Kiel, Department of Economics.
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