Best Practice Recommendation for Forecasting Counts

The existing techniques of forecasting a future count either treat the time series of counts as a Gaussian time series or use a random effects based dynamic Poisson model. The normality based approach may not yield valid forecasting, whereas the random effects based model usually generates a complex correlation structure for the time series of counts which may be impractical to use for forecasting. Moreover, when the time series contains moderately large or large counts, the later random effects based models are known to be inefficient in forecasting a future count, based on such a time series of large counts. In this report, we propose an observation driven non-stationary correlation model to fit a time series of counts with possible overdispersion. Analogoues to the Gaussian time series techniques, we develop forecasting functions to forecast future counts. The proposed forecasting approach is simpler than the existing approaches and it is shown through a simulation study that this approach provides satisfactory forecasting for a future count, irrespective of the cases whether time series contains small or large counts. Thus, the proposed approach may be recommended as the best practical approach for forecasting a count. The forecasting methodology is illustrated by analyzing a U.S. time series of polio counts. Some key words: Consistency; Efficiency; Latent process driven longitudinal correlation; Observations driven longitudinal autocorrelation; Overdispersion; Regression effects; Forecasting.