In the era of big data, there is an increasing demand for new methods for analyzing and forecasting 2-dimensional data. The current research aims to accomplish these goals through the combination of time-series modeling and multilinear algebraic systems. We expand previous autoregressive techniques to forecast multilinear data, aptly named the L-Transform Tensor autoregressive (L-TAR for short). Tensor decompositions and multilinear tensor products have allowed for this approach to be a feasible method of forecasting. We achieve statistical independence between the columns of the observations through invertible discrete linear transforms, enabling a divide and conquer approach. We present an experimental validation of the proposed methods on datasets containing image collections, video sequences, sea surface temperature measurements, stock prices, and networks.
Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Series
Department of Mathematics, Pusan National University, Republic of Korea（釜山国立大学数学系）；Pusan National University, Republic of Korea（釜山国立大学）；Industrial Mathematics Center, Pusan National University, Republic of Korea（釜山国立大学工业数学中心）；Humanoid Olfactory Display Center, Pusan National University, Republic of Korea（釜山国立大学人形嗅觉显示中心）；Department of Mathematics, Yonsei University, Republic of Korea（成均馆大学数学系）；Innovation Center for MathScience Research&Education, Pusan National University, Republic of Korea（釜山国立大学数学科学研究与教育创新中心）；Marine Natural Disaster Research Department, Korea Institute of Ocean Science and Technology, Republic of Korea（韩国海洋科学与技术研究院海洋自然灾害研究部）；Institute for Future Earth, Pusan National University, Republic of Korea（未来地球研究所）
ARMA Block: A CNN-Based Autoregressive and Moving Average Module for Long-Term Time Series Forecasting
AI Lab, Grepp（Grepp人工智能实验室）；Department of Computer Science and Engineering, Hankuk University of Foreign Studies（韩国外国语大学计算机科学与工程系）；Department of Radiation Physics, The University of Texas MD Anderson Cancer Center（德克萨斯MD安德森癌症中心辐射物理系）
Sparsity-Induced Global Matrix Autoregressive Model with Auxiliary Network Data
The University of Hong Kong（香港大学）；Faculty of Business and Economics, The University of Hong Kong（香港大学商学院）；Department of Statistics and Actuarial Science, The University of Hong Kong（香港大学统计与精算学系）
