Bayesian Prediction of Autoregressive Models Using Different Types of Priors

M.Shaarawy, Samir; E.A.Soliman, Emad; E.A.Shahin, Heba

doi:10.21608/esju.2010.314306

Bayesian Prediction of Autoregressive Models Using Different Types of Priors

Document Type : Original Article

Authors

¹ Department of Mathematical Sciences, Umm El-Qura University, Mekka, Kingdom of Saudi Arabia.

² Department of Statistics, King Abdul Aziz University, Jeddah, Kingdom of Saudi Arabia.

³ Researcher Sector, Central Bank of Egypt, Cairo, Egypt.

10.21608/esju.2010.314306

Abstract

The current study approaches the Bayesian prediction of autoregressive processes using three well-known priors; g-prior, natural conjugate (NC)) prior, and Jeffreys' prior. The main goal of the study is to derive the one step-ahead predictive densities in case of autoregressive (AR) models using each of the above mentioned priors. However, the basic contribution is the derivation of the predictive density based upon the g-prior. Investigating the performance of the three on step-ahead predictive densities is performed via simulation studies using AR (1) and AR (2) processes for illustration. The simulation results show the equivalence of the performance of the three one step-ahead predictive densities based on the three considered priors in the forecasting process.

Keywords