Multilinear Low-Rank Vector Autoregressive Modeling via Tensor Decomposition

• Activity Number: 177 - Section on Statistical Learning and Data Science CPapers 2
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Di Wang* and Guodong Li and Dr. LIAN Heng
• Companies: University of Hong Kong and University of Hong Kong and City University of Hong Kong
• Keywords: Dimension reduction; High dimensional time series; Higher order singular value decomposition; Reduced-rank model; Regularization; Tucker decomposition

Abstract

The classical Vector Autoregressive (VAR) model has a large number of parameters so it can suffer from the curse of dimensionality for high-dimensional time series data. The reduced-rank coefficient model can alleviate the problem but the low-rank structure along the time direction for time series models has never been considered. In this paper, we rearrange the parameters in the VAR model to a tensor form, and propose a multilinear low-rank VAR model via tensor decomposition that effectively exploits the temporal and cross-sectional low-rank structure. Under this framework, an alternating least squares algorithm is developed for maximum likelihood estimation in the low-dimensional case and its asymptotic properties are studied. For the high-dimensional and large-scaled time series data, we develop a Sparse Higher-Order Reduced-Rank (SHORR) estimator to further reduce the number of parameters and perform variable selection. The non-asymptotic error bound for the SHORR estimator is established and an ADMM-based algorithm is proposed. Effectiveness of the methods is demonstrated on simulated and real data.