Vector Error Correction Model (VECM) is a classic method to analyse cointegration relationships amongst multivariate non-stationary time series. In this paper, we focus on high dimensional setting and seek for sample-size-efficient methodology to determine the level of cointegration. Our investigation centres at a Bayesian approach to analyse the cointegration matrix, henceforth determining the cointegration rank. We design two algorithms and implement them on simulated examples, yielding promising results particularly when dealing with high number of variables and relatively low number of observations. Furthermore, we extend this methodology to empirically investigate the constituents of the S&P 500 index, where low-volatility portfolios can be found during both in-sample training and out-of-sample testing periods.

翻译：向量误差修正模型（VECM）是分析多元非平稳时间序列间协整关系的经典方法。本文聚焦于高维设定，寻求能够确定协整程度的样本高效方法论。我们的研究核心在于采用贝叶斯方法分析协整矩阵，进而确定协整秩。我们设计了两种算法并在模拟实例上实施，尤其在变量数量较多而观测值相对较少的情况下取得了令人满意的结果。此外，我们将该方法扩展到对标准普尔500指数成分股的实证研究中，发现在样本内训练和样本外测试期间均可构建低波动率投资组合。