Multiple Time Series Modeling Using the SAS VARMAX Procedure

Chapter 12: Bayesian Vector Autoregressive Models

Introduction

The Prior Covariance of the Autoregressive Parameter Matrices

The Prior Distribution for the Diagonal Elements

The Prior Distribution for the Off-Diagonal Elements

The BVAR Model in PROC VARMAX

Specific Parameters in the Prior Distribution

Further Shrinkage toward Zero

Application of the BVAR(1) Model

BVAR Models for the Egg Market

Conclusion

Introduction

One way to reduce the number of parameters in a Vector Autoregressive Moving Average, VARMA(p,q), model that has no moving average terms, q = 0, is to consider Bayesian estimation. The idea is that an informative prior is applied to the autoregressive parameters, usually in order to shrink them toward zero. The prior distribution ...