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Title: High-dimensional matrix autoregressive model Authors:  Di Wang - University of Hong Kong (Hong Kong) [presenting]
Guodong Li - University of Hong Kong (Hong Kong)
Abstract: High-dimensional matrix-valued time series data are getting widely available in many fields, such as macroeconomics, finance and image processing. It is natural to vectorize the matrix-valued data and apply the classic vector autoregressive model, but the model will suffer from the curse of dimensionality for high-dimensional data. We propose a matrix autoregressive model by folding the parameter matrix to a fourth-order tensor and consider a multilinear low rank structure for the parameter tensor to achieve substantial dimension reduction. Under the fixed dimension scenario, we study the asymptotic properties of the least squares estimator with low-rank constraints. For the case with much higher dimension, a novel convex regularization approach is proposed for estimation and the oracle inequalities are established. The methods can be readily extended to the high-dimensional tensor autoregressive model.