Multi-linear Tensor Autoregressive Models

• DOI: 10.48550/arxiv.2110.00928
• Publication Date: 2021-01-01
• Authors: Zebang Li; Xiao Han
• Keywords: Methodology (stat.ME); FOS: Computer and information sciences; 0101 mathematics; 01 natural sciences; Statistics - Methodology

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