Predictive likelihood for coherent forecasting of count time series

Abstract

AbstractA new forecasting method based on the concept of the profile predictive likelihood function is proposed for discrete‐valued processes. In particular, generalized autoregressive moving average (GARMA) models for Poisson distributed data are explored in detail. Highest density regions are used to construct forecasting regions. The proposed forecast estimates and regions are coherent. Large‐sample results are derived for the forecasting distribution. Numerical studies using simulations and two real data sets are used to establish the performance of the proposed forecasting method. Robustness of the proposed method to possible misspecifications in the model is also studied.