In this paper, we perform multivariate time series analysis from a Bayesian machine learning perspective through the proposed multivariate Bayesian time series (MBTS) model. The multivariate structure and the Bayesian framework allow the model to take advantage of the association structure among target series, select important features, and train the data-driven model at the same time. Extensive analyses on both simulated data and empirical data indicate that the MBTS model is able to, cover the true values of regression coefficients in 90% credible intervals, select the most important predictors, and boost the prediction accuracy with higher correlation in absolute value of the target series, and consistently yield superior performance over the univariate Bayesian structural time series (BSTS) model, the autoregressive integrated moving average with regression (ARIMAX) model, and the multivariate ARIMAX (MARIMAX) model, in one-step-ahead forecast and ten-steps-ahead forecast.

中文翻译：

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贝叶斯机器学习视角下的多元时间序列分析

在本文中，我们通过提出的多元贝叶斯时间序列 (MBTS) 模型从贝叶斯机器学习的角度进行多元时间序列分析。多元结构和贝叶斯框架使模型能够利用目标序列之间的关联结构，选择重要特征，同时训练数据驱动模型。对模拟数据和经验数据的广泛分析表明，MBTS 模型能够在 90% 的可信区间内覆盖回归系数的真实值，选择最重要的预测变量，并通过更高的绝对值相关性来提高预测精度。目标序列，并始终比单变量贝叶斯结构时间序列 (BSTS) 模型产生更好的性能，