Analysis of Tensor Time Series

Abstract

This article provides a comprehensive overview of statistical methods developed for the analysis of tensor time series data, which have become increasingly prevalent across various fields such as economics, finance, biology, engineering, and the social sciences. The review focuses on three primary approaches: autoregressive modeling, factor modeling, and segmentation approaches. These methods leverage the inherent tensor structure to offer advantages such as dimension reduction, enhanced interpretability, and computational efficiency. The review focuses on model settings and their potential interpretations, discussing various estimation techniques for these models and their associated theoretical properties. In addition, we outline various applications using these models and discuss potential directions for future developments.