Assessment of forecasts and forecast uncertainty using generalized linear regression models for time series count data

This paper evaluates a prediction methodology for forecasting non-Gaussian time series count data using quasi-likelihood regression models. A detailed simulation study is used to assess the accuracy of forecasts from the quasi-likelihood predictor, and to study the effect of several different specifications of the variance-covariance matrix in the quasi-likelihood approach. Effects due to the strength of the autocorrelation and overdispersion on the accuracy of the forecasts are also investigated. Forecasts and forecast uncertainty obtained using the quasi-likelihood predictor are also compared to those obtained using the traditional best linear unbiased predictor (BLUP). Results from this investigation show that the quasi-likelihood predictors give fairly accurate results in a variety of situations and give more accurate forecasts than the BLUP, regardless of the magnitude of the overdispersion, the strength of the autocorrelation, or the nature of the mean function. These results also show that the measure of forecast error associated with the quasi-likelihood predictor more realistically reflects the true variability in the forecast error than that corresponding to the BLUP. Overall, the quasi-likelihood prediction methodology is fairly accurate for forecasting time series count data and may also be an accurate and flexible approach for forecasting other types of non-Gaussian time series data.