System Identification of High-Dimensional Linear Dynamical Systems With Serially Correlated Output Noise Components
System Identification of High-Dimensional Linear Dynamical Systems With Serially Correlated Output Noise Components
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DOI：
10.1109/tsp.2020.3020397
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发表时间：
2020-08
影响因子：
5.4
通讯作者：
Jiahe Lin;G. Michailidis
中科院分区：
文献类型：
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作者：
Jiahe Lin;G. Michailidis
我们考虑识别的线性动力系统，包括高维信号，其中的输出噪声分量表现出很强的串行，横截面的相关性。虽然这样的设置出现在许多现代应用中，但这样的依赖结构尚未完全并入文献中的现有方法中。在本文中，我们明确地将依赖结构中存在的输出噪声通过滞后值的观测到的多元信号。我们制定了一个约束优化问题，以确定由潜在状态跨越的空间，并同时滞后值的转移矩阵，其中的约束反映了低秩性质的状态信息，和稀疏的转移矩阵。我们建立了估计量的理论性质，并为经验应用引入了一个易于实现的计算程序。所提出的方法的性能，以及实施程序的合成数据进行评估，并与竞争的方法进行比较，并进一步说明了一个数据集，涉及75个美国大型金融机构的2001年至2017年期间的每周股票收益率。
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.