Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight to the model structure and may lead to highly noisy estimates of the parameters. Because of these limitations, there has been an increasing interest towards methods that produce sparse estimates through penalized regression. However, such methods are computationally intensive and may become prohibitively time-consuming when the number of variables in the model increases. In this paper we adopt an approximate Bayesian approach to the learning problem by combining fractional marginal likelihood and pseudo-likelihood. We propose a novel method, PLVAR, that is both faster and produces more accurate estimates than the state-of-the-art methods based on penalized regression. We prove the consistency of the PLVAR estimator and demonstrate the attractive performance of the method on both simulated and real-world data.

翻译：多变时间序列的学习矢量自动递减模型通常通过最小平方或最大可能性估计来对待。这些方法通常假设一个完全相连的模型,不直接洞察模型结构,并可能导致对参数的高度噪音估计。由于这些限制,人们越来越关注通过惩罚性回归产生稀疏估计数的方法。然而,这些方法在计算上是密集的,在模型变数增加时可能会变得令人望而却步地耗时。在本文中,我们采用一种近似巴伊西亚的方法解决学习问题,将微小可能性和假相似性结合起来。我们提出了一个新颖的方法,即PLVAR,该方法比基于惩罚性回归的最先进的方法更快和产生更准确的估计数。我们证明了PLVAR估计器的一致性,并展示了模拟数据和真实世界数据方法的吸引力。