### Modelling Time Series Count Data: An Autoregressive (2003)Modelling Time Series Count Data: An Autoregressive (2003)

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 Author Heinen, Andréas Source CiteSeerX Content type Text File Format PDF Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Straightforward Likelihood Ratio Test ♦ Good Density Forecast ♦ Improved Inference ♦ First Step ♦ Double Poisson Distribution ♦ Ibm Stock ♦ Marginal Distribution ♦ Usual Test ♦ Maximum Likelihood ♦ Second Step ♦ Dispersion Parameter Time-varying ♦ Main Concern ♦ Additional Dispersion Parameter ♦ Price Change Duration ♦ Flexible Way ♦ Stock Price ♦ Static Poisson Regression ♦ Paper Introduces ♦ Framework Autocorrelation ♦ Autoregressive Conditional Poisson Model ♦ Price-change Duration ♦ New Model ♦ Acp Model ♦ Parametric Approach ♦ Intradaily Volatility ♦ Sharp Contrast ♦ Exogenous Regressors ♦ Time Series ♦ Daily Number ♦ Monthly Polio Case ♦ Test Procedure ♦ Time Series Count Data ♦ Past Observation ♦ Serial Correlation Description 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. Educational Role Student ♦ Teacher Age Range above 22 year Educational Use Research Education Level UG and PG ♦ Career/Technical Study Learning Resource Type Article Publisher Date 2003-01-01 Publisher Institution Conditional Poisson Model. CORE Discussion Paper