On forecasting counts

Forecasting for a time series of low counts, such as forecasting the number of patents to be awarded to an industry, is an important research topic in socio-economic sectors. Recently (2004), Freeland and McCabe introduced a Gaussian type stationary correlation model-based forecasting which appears to work well for the stationary time series of low counts. In practice, however, it may happen that the time series of counts will be non-stationary and also the series may contain over-dispersed counts. To develop the forecasting functions for this type of non-stationary over-dispersed data, the paper provides an extension of the stationary correlation models for Poisson counts to the non-stationary correlation models for negative binomial counts. The forecasting methodology appears to work well, for example, for a US time series of polio counts, whereas the existing Bayesian methods of forecasting appear to encounter serious convergence problems. Further, a simulation study is conducted to examine the performance of the proposed forecasting functions, which appear to work well irrespective of whether the time series contains small or large counts. Copyright © 2008 John Wiley & Sons, Ltd.