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.