Volume 16, Issue 30, Autumn 2019
IRAQI JOURNAL OF STATISTICAL SCIENCES,
Volume 16, Issue 30, Pages 1-24
In many applications of time series , the white noise does not follow the normal distribution but follows one of the heavy tailed distributions. When
using normal models in estimation and forecasting, these phenomena they will produce far from reality and inefficient estimators and predictions. The generalized multivariate modified Bessel distribution belongs to the potentially heavy-tailed distribution family and has wide applications in events that change over time. On this basis, this paper concerned with the study of vector moving average model of the first order (VMA(1)), is the white noise error term of this model follows GMMB. The non linear VMA(1) model was approximated to a linear model. The parameters of approximated model was estimated by Bayesian technique when non-informative priors. We supposed that some parameters of the distribution ( ) known.
Different loss functions has been used in Bayesian analysis, We proposed two positive weight functions in weighted balanced loss functions .
Some of theoretical results were applied on empirical sample generated from VMA(1) model. It is concluded that the estimators under proposed weighted balanced loss functions are better.