Optimal Bayesian Regression for Serially Dependent Training Observations

In this study, we construct, for the first time, the optimal Bayesian Regression (OBR) when the training data are serially dependent. To model the effect of dependency, we assume the training data are generated from
$\text{VAR} (p)$
, which is a multi-dimensional vector autoregressive process of order
$p$
. Our numerical experiments show that when the training samples follow a VAR dependency model, the proposed regressor can outperform the usual regressor, which is developed under sample independence assumption.