Zebang Li, Rutgers University
Project Description/Abstract
Contemporary time series analysis has seen more and more tensor type data, from many fields. For example, stocks can be grouped according to size, book-to-market ratio, and operating profitability, leading to a 3-way tensor observation each month. We propose an autoregressive model for the tensor-valued time series, with autoregressive terms depending on multi-linear coefficient matrices. Comparing with the traditional approach of vectoring the tensor observations and then applying the vector autoregressive model, the tensor autoregressive model preserves the tensor structure and admits corresponding interpretations. We introduce three estimators based on projection, least squares, and maximum likelihood. Our analysis considers both fixed dimensional and high dimensional settings. For the former, we establish the central limit theorems of the estimators, and for the latter, we focus on the convergence rates and the model selection. The performance of the model is demonstrated by simulated and real examples.
Co-authors
Han Xiao, Rutgers University