Bayesian Estimation of Multivariate Pure Moving Average Processes

Abstract

The multivariate estimation problems arise if the observations are available for several related variables of interest. The multivariate time series may be found in many fields of application such as economics, meteorology and utilities. The current study has three main objectives. The first one is to develop an approximate convenient Bayesian methodology to estimate the parameters of multivariate moving average processes. The second objective is to investigate the numerical efficiency of the proposed technique in solving the estimation problems by conducting a wide simulation study. The last objective is to study the sensitivity of the numerical efficiency with respect to the parameters values and time series length. The results show that the proposed technique succeeded in estimating the parameters of the multivariate moving average processes. The results are not sensitive to the changes in parameter values or in time series length.

Keywords

• Multivariate time series
• multivariate (vector) moving average processes
• Bayesian estimation
• matrix normal-Wishart prior
• Jeffreys’ prior