Forecasting demand for health services: Development of a publicly available toolbox

A publicly available toolbox to forecast count data is developed in this work. The toolbox is implemented in MATLAB environment with the newly developed generalized autoregressive moving average (GARMA) models with discrete-valued distributions. GARMA models treat count data in a mathematically coherent manner compared to Gaussian models, often inappropriately applied in health care applications. GARMA models can incorporate none to many exogenous variables hypothesized to influence the predicted responses (i.e., counts forecasted). The toolbox's primary purpose is to deliver one to multiple-steps ahead forecasts, but also gives information for model inference and validation. The toolbox uses the maximum likelihood method to estimate model parameters from the data. We demonstrate toolbox application and validity on two example health care count data sets and show how using integer-valued conditional distributions as offered by GARMA models can produce forecast models that outperform the traditional Gaussian models.