We consider identification of linear dynamical systems comprising of high-dimensional signals, where the output noise components exhibit strong serial, and cross-sectional correlations. Although such settings occur in many modern applications, such dependency structure has not been fully incorporated in existing approaches in the literature. In this paper, we explicitly incorporate the dependency structure present in the output noise through lagged values of the observed multivariate signals. We formulate a constrained optimization problem to identify the space spanned by the latent states, and the transition matrices of the lagged values simultaneously, wherein the constraints reflect the low rank nature of the state information, and the sparsity of the transition matrices. We establish theoretical properties of the estimators, and introduce an easy-to-implement computational procedure for empirical applications. The performance of the proposed approach, and the implementation procedure is evaluated on synthetic data, and compared with competing approaches, and further illustrated on a data set involving weekly stock returns of 75 US large financial institutions for the 2001–2017 period.

中文翻译：

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具有串行相关输出噪声分量的高维线性动力系统的系统辨识

我们考虑识别由高维信号组成的线性动力系统，其中输出噪声分量表现出很强的串行和横截面相关性。尽管此类设置出现在许多现代应用程序中，但此类依赖结构尚未完全纳入文献中的现有方法。在本文中，我们通过观察到的多元信号的滞后值明确地合并了输出噪声中存在的依赖结构。我们制定了一个约束优化问题来同时识别潜在状态跨越的空间和滞后值的转移矩阵，其中约束反映了状态信息的低秩性质和转移矩阵的稀疏性。我们建立估计量的理论性质，并为经验应用引入易于实现的计算程序。所提出方法的性能和实施程序在综合数据上进行了评估，并与竞争方法进行了比较，并在涉及 75 家美国大型金融机构 2001 年至 2017 年期间每周股票收益的数据集上进行了进一步说明。