An effectiveness study of the Bayesian inference with multivariate autoregressive moving average processes

Abstract

Multivariate time series may be found in many fields of application such as economics, meteorology, and utilities. In economics, for example, one may record yearly money supply and real interest rate. These variables are modeled, and the parameters are estimated jointly to understand the nature of the dynamic relationships between variables and increase the precisions of the estimates. Better estimates can be achieved when the series are modeled jointly if there is information on one series contained in the others. Shaarawy has introduced an analytical approximate Bayesian methodology for the statistical inference of multivariate autoregressive moving average (VARMA) processes. The main objective of the current study is to investigate the numerical effectiveness of his proposed methodology in solving the estimation problems of multivariate VARMA processes by conducting a wide simulation study. Moreover, the study investigates the sensitivity of the numerical effectiveness of the proposed methodology with respect to the parameters’ values and time series length. Simulation results showed that the methodology succeeded in estimating the parameters of VARMA models, for all parameters’ values and time series lengths.

Keywords:

• Bayesian inference
• Estimation
• Jeffreys’ prior
• Matrix t distribution
• Matrix Normal-Wishart prior
• Multivariate autoregressive moving average processes

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60E05
• Secondary 62M10

Acknowledgements

This Project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (G: 280-130-1440). The authors, therefore, acknowledge with thanks DSR for technical and financial support.