Forecasting overdispersed count time series with the DLD-INAR(1) model

Abstract

This paper investigates coherent forecasting of overdispersed count data using the stationary DLD-INAR(1) process. Although the process has been introduced previously, we extend the existing literature by establishing its k-step-ahead predictive properties and the corresponding predictive probability distribution. Based on this, we develop forecasting procedures using median and mode predictors, with parameters estimated via conditional maximum likelihood. The main contribution of this manuscript lies in the comprehensive evaluation of forecasting performance. Through simulation studies using PRMSE, PMAE, and PTP metrics, we show that forecasts based on the median and mode outperform those based on the mean. Finally, we demonstrate the practical relevance of our results through a real data application, comparing the predictive accuracy of the DLD-INAR(1) process with that of the GINAR(1) and PINAR(1) models.