Optimal Bayesian Regression With Vector Autoregressive Data Dependency
Abstract: 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.
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