Time series forecasts of ambulance run volume

To test the hypothesis that time series analysis can provide accurate predictions of future ambulance service run volume, a prospective stochastic time series modeling study was conducted at a community-based regional ambulance service. For all requests for ambulance transport during two sequential years, the time and date, total run time, and acuity code of the run were recorded in a computer database. Time series variables were formed for ambulance service runs per hour, total run time, and acuity. Prediction models were developed from one complete year's data (1994) and included four model types: raw observations, moving average, means with moving average smoothing, and autoregressive integrated moving average. Forecasts from each model were tested against observations from the first 24 weeks of the subsequent year (1995). Each model's adequacy was tested on residuals by autocorrelation functions, integrated periodograms, linear regression, and differences among the variances. A total of 68,433 patients were seen in 1994 and 32,783 in the first 24 weeks of 1995. Large periodic variations in run volume with time of day were found (P < .001). A model based on arithmetic means of each hour of the week with 3-point moving average smoothing yielded the most accurate forecasts and explained 54.3% of the variation observed in the 1995 test series (P < .001). Time series analysis can provide powerful, accurate short-range forecasts of future ambulance service run volume. Simpler, less expensive models performed best in this study.