Predictive Likelihood for Coherent Forecasting of Count Time Series

TL;DR

This paper introduces a novel forecasting approach for count time series using profile predictive likelihood, focusing on GARMA models for Poisson data, with proven large sample properties and validated through simulations and real data.

Contribution

It develops a coherent forecasting method based on profile predictive likelihood for discrete count data, including GARMA models, with theoretical and empirical validation.

Findings

The method provides coherent forecasts and regions.

Large sample properties are established.

Numerical studies demonstrate robust performance.

Abstract

A new forecasting method based on the concept of the profile predictive the likelihood function is proposed for discrete-valued processes. In particular, generalized autoregressive and moving average (GARMA) models for Poisson distributed data are explored in details. 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 a real data set are used to establish the performance of the proposed forecasting method. Robustness of the proposed method to possible misspecification in the model is also studied.