BAYESIAN ESTIMATION FOR ARMA MODELS

Abstract

The concept of estimating a parameter is needed to help estimate a situation or observational data before making a decision.  There are estimation methods that have been developed, namely the moment method, which is the oldest method, the maximum likelihood method (MLE), and the Bayes method, which is the latest method in determining the estimator of a parameter.  Furthermore, the concept of forecasting is also one of the important ways to make a decision.  Time series analysis technique (time series) is one of the forecasting methods that are often used, were specifically selected ARMA models.  In the Bayesian approach, the parameters in the ARMA model are seen as quantities whose variance is represented by a probability distribution called a prior distribution.  Within the framework of Bayes decision theory, estimator selection can be thought of as a problem of decision theory in uncertain circumstances.  By using a multivariate Wishart normal prior distribution, the Bayesian estimator for  is  = z + u* and the Bayesian estimator for is: , with L = (1,0,…,0)’  and S_* = S + Using the Gamma multivariate prior normal distribution, the Bayesian estimator for is  = Z + u_o and the Bayesian estimator for  is :  =  , with u₀ = (s u + R y), _* = Forecasting one step ahead, namely: _n(I)