Regularized High-Dimensional Additive Tensor Autoregressive Model

2026-08-26

AI Summary

本文提出了一种正则化加性张量自回归模型，通过行、列和管方向的时间依赖性的加性交互作用来提高解释性和减少计算负担，并估计转移矩阵的低秩加稀疏模式。

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 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.

Problem

• High-dimensional time series
• Tucker-decomposition
• temporal dependence

Innovation

• Additive Tensor Autoregressive Model
• Interpretability
• Convex Optimization
• Low Rank Plus Sparse Pattern
• Alternating Block Minimization