Title: High-Dimensional Regularized Additive Matrix Autoregressive Model Show Chinese title

Title: 高维正则化加性矩阵自回归模型

Abstract: High-dimensional time series has diverse applications in econometrics and finance. Recent models for capturing temporal dependence have employed a bilinear representation for matrix time series, or the Tucker-decomposition based representation in case of tensor time series. A bilinear or Tucker-decomposition based temporal effect is difficult to interpret on many occasions, along with its computational complexity due to the non-convex nature of the underlying optimization problem. Moreover, the existing matrix case models have not sufficiently explored the possibilities of imposing any lower-dimensional pattern on the transition matrices. In this work, we propose a regularized additive matrix autoregressive model with additive interaction of row-wise and column-wise temporal dependence, that offers more interpretability, less computational burden due to its convex nature and estimation of the underlying low rank plus sparse pattern of its transition matrices. We address the issue of identifiability of the various components in our model and subsequently develop a scalable Alternating Block Minimization algorithm for estimating the parameters. We provide a finite sample error bound under high-dimensional scaling for the model parameters. Finally, the efficacy of the proposed model is demonstrated on synthetic and real data. Show Chinese abstract

Abstract: 高维时间序列在计量经济学和金融领域有着广泛的应用。 近年来用于捕捉时间依赖性的模型采用了矩阵时间序列的双线性表示，或者张量时间序列基于Tucker分解的表示方法。然而，基于双线性或Tucker分解的时间效应在许多情况下难以解释，并且由于其优化问题的非凸性质导致计算复杂度较高。此外，现有的矩阵案例模型尚未充分探索在转移矩阵上施加低维模式的可能性。 在本研究中，我们提出了一种正则化的加法矩阵自回归模型，该模型具有行间和列间时间依赖性的加法交互作用，这提供了更高的可解释性，由于其凸性降低了计算负担，并估计了转移矩阵的潜在低秩加稀疏模式。我们解决了模型中各个组件的可识别性问题，并随后开发了一种可扩展的交替块最小化算法来估计参数。我们还提供了模型参数在高维尺度下的有限样本误差界。最后，通过合成数据和真实数据验证了所提出的模型的有效性。