A key input to the call center staffing process is a forecast for the number of calls arriving. Density forecasts of arrival rates are needed for analytical call center models, which assume Poisson arrivals with a stochastic arrival rate. Density forecasts of call volumes can be used in simulation models and are also important for the analysis of outsourcing contracts. A forecasting method, which has previously shown strong potential, is Holt--Winters exponential smoothing adapted for modeling the intraday and intraweek cycles in intraday data. To enable density forecasting of the arrival volume and rate, we develop a Poisson count model, with gamma distributed arrival rate, which captures the essential features of this exponential smoothing method. The apparent stationary level in our data leads us to develop versions of the new model for series with stationary levels. We evaluate forecast accuracy up to two weeks ahead using data from three organizations. We find that the stationary level models improve prediction beyond approximately two days ahead, and that these models perform well in comparison with sophisticated benchmarks. This is confirmed by the results of a call center simulation model, which demonstrates the use of arrival rate density forecasting to support staffing decisions.