This paper introduces and evaluates new models for time series count data. The Autoregressive Conditional Poisson model makes it possible to deal with issues of discreteness, overdispersion (variance greater than the mean) and serial correlation. A variety of models, based on the double Poisson distribution is introduced, which introduce an additional dispersion parameter and at a later stage make it time-varying. The models are applied to a medical series as well as to the daily number of price change durations of $.75, thus providing a volatility model based on intradaily data. It is shown that the model provides very good density forecasts.