  We introduce a new method for forecasting emergency call arrival rates that
combines integer-valued time series models with a dynamic latent factor
structure. Covariate information is captured via simple constraints on the
factor loadings. We directly model the count-valued arrivals per hour, rather
than using an artificial assumption of normality. This is crucial for the
emergency medical service context, in which the volume of calls may be very
low. Smoothing splines are used in estimating the factor levels and loadings to
improve long-term forecasts. We impose time series structure at the hourly
level, rather than at the daily level, capturing the fine-scale dependence in
addition to the long-term structure. Our analysis considers all emergency
priority calls received by Toronto EMS between January 2007 and December 2008
for which an ambulance was dispatched. Empirical results demonstrate
significantly reduced error in forecasting call arrival volume. To quantify the
impact of reduced forecast errors, we design a queueing model simulation that
approximates the dynamics of an ambulance system. The results show better
performance as the forecasting method improves. This notion of quantifying the
operational impact of improved statistical procedures may be of independent
interest.
