Optimal Bayesian Regression With Vector Autoregressive Data Dependency

In this study, we derive a closed-form analytic representation of the optimal Bayesian regression when the data are generated from text{VAR}(p), which is a multidimensional vector autoregressive process of order p. Given the covariance matrix of the underlying Gaussian white-noise process, the developed regressor reduces to the conventional optimal regressor for a non-informative prior and setting p=0, which implies independent data. Our empirical results using both synthetic and real data show that the developed regressor can effectively be used in situations where the data are sequentially dependent.