Transform-Based Tensor Auto Regression for Multilinear Time Series Forecasting

With the massive influx of 2-dimensional observational data, new methods for analyzing, modeling, and forecasting multidimensional data need to be developed. The current research aims to accomplish these goals through the intersection of time-series modeling and multi-linear algebraic systems. In particular, the current research, aptly named the $\mathcal{L}$-Transform Tensor Auto-Regressive ($\mathcal{L}$-TAR for short) model expands previous auto-regressive techniques to forecast data from multilinear observations as oppose to scalars or vectors. The approach is based on recent developments in tensor decompositions and multilinear tensor products. Transforming the multilinear data through invertible discrete linear transforms enables statistical Independence between observations. As such, can be reformulated to a collection of vector auto-regression problems for model learning. Experimental results are provided on benchmark datasets containing image collections, video sequences, sea surface temperature measurements, and stock closing prices.