In this study, we derive a closed-form analytic representation of the optimal Bayesian regression when the data are generated from VAR(p)\text{VAR}(p), which is a multidimensional vector autoregressive process of order pp. 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=0p=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.

中文翻译：

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具有向量自回归数据依赖性的最优贝叶斯回归


在本研究中，当数据从 VAR(p)\text{VAR}(p) 生成时，我们推导出最优贝叶斯回归的封闭式解析表示，这是一个 pp 阶的多维向量自回归过程。给定协方差基础高斯白噪声过程的矩阵，开发的回归器减少到非信息先验的传统最优回归器并设置 p=0p=0，这意味着独立数据。我们使用合成数据和真实数据的实证结果表明，所开发的回归器可以有效地用于数据顺序相关的情况。