AI 中文总结
针对高维时间序列分析，提出正则化可加张量自回归模型，通过交替块极小化算法估计参数，在合成与真实数据上验证其有效性，兼具可解释性与低计算负担。
AI 中文摘要
高维时间序列在计量经济学和金融学中有广泛应用。近期用于捕捉时间依赖性的模型，对矩阵时间序列采用双线性表示，对张量时间序列则采用基于Tucker分解的表示。基于Tucker分解的时间效应在许多情况下难以解释，且由于底层优化问题的非凸性，计算复杂度较高。此外，现有张量模型尚未充分探索在转移矩阵上施加任何低维模式的可能性。本研究中，我们提出一种正则化可加张量自回归模型，具有行方向、列方向和管方向时间依赖性的可加交互作用，该模型因凸性而提供更强的可解释性、更低的计算负担，并能估计其转移矩阵的底层低秩加稀疏模式。我们解决了模型中各成分的可识别性问题，随后开发了一种可扩展的交替块极小化算法用于参数估计。我们在高维尺度下为模型参数提供了有限样本误差界。最后，通过合成数据和真实数据验证了所提模型的有效性。
英文摘要
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 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 tensor 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 tensor autoregressive model with additive interaction of row-wise, column-wise and tube-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.
