The Coefficient Estimation of Tensor Autoregression Based on TR Decomposition

With the advent of tensor-valued time series data, tensor autoregression appears in many fields, in which the coefficient estimation is confronted with the problem of dimensional disaster. Based on the tensor ring (TR) decomposition, an autoregression model with one order for tensor-valued responses is proposed in this paper. A randomized method, TensorSketch, is applied to the TR autoregression model for estimating the coefficient tensor. Convergence and some properties of the proposed methods are given. Finally, some numerical experiment results on synthetic data and real data are given to illustrate the effectiveness of the proposed method.