Abstract
The main purpose of this study is to find the Bayesian forecast of ARMA model under Jeffrey's prior assumption with quadratic loss function. The point forecast model is to obtained based on the mean of the marginal conditional posterior predictive in mathematical expression. Furthermore, the point forecast model of the Bayesian forecasting compared to the traditional forecasting. The simulation shows that the forecast accuracy of the Bayesian forecasting is better than the traditional forecasting and the descriptive statistics of the Bayesian forecasting are closer to the true value than the traditional forecasting.
Highlights
The Bayesian approach in general requires explicit formulation of a model and conditioning on known quantities in order to draw inferences about unknown ones
There are three steps are accomplished in the process of fitting the ARMA (p, q) model to a time series identification of the model, estimation of the parameters, and model checking to conclude whether the models obtained are adequate for forecasting
Several of works relating to Bayesian forecasting in the ARMA model are Fan & Yao [8] and Uturbey [13] using ARMA with normal-gamma prior
Summary
The Bayesian approach in general requires explicit formulation of a model and conditioning on known quantities in order to draw inferences about unknown ones. There are three steps are accomplished in the process of fitting the ARMA (p, q) model to a time series identification of the model, estimation of the parameters, and model checking to conclude whether the models obtained are adequate for forecasting. Several of works relating to Bayesian forecasting in the ARMA model are Fan & Yao [8] and Uturbey [13] using ARMA with normal-gamma prior. Kleibergen & Hoek [11], Liu [13], and Mohamed et al [14] using ARMA model with Jeffrey's prior. This paper focuses on the Bayesian multiperiod forecasting for ARMA model using Jeffrey’s prior with quadratic loss function
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