A0284
Title: High-dimensional low-rank linear time series modeling
Authors: Guodong Li - University of Hong Kong (Hong Kong) [presenting]
Abstract: Low-rank structures are imposed to the column and row spaces of coefficient matrices in a multivariate infinite-order vector autoregression (VAR), which, with the help of tensor techniques, leads to a newly proposed concept of supervised factor models, where two-factor modelings are conducted to responses and predictors simultaneously. Interestingly, the stationarity condition implies an intrinsic weak group sparsity mechanism of infinite-order VAR, and hence a rank-constrained group Lasso estimation is considered to make inferences on high-dimensional time series. Its non-asymptotic properties are also discussed thoughtfully by balancing the estimation, approximation and truncation errors. Moreover, an alternating gradient descent algorithm with thresholding is designed to search for the high-dimensional estimate, and its theoretical justifications, including statistical and convergence analysis, are also provided. Theoretical and computational properties of the proposed methodology are verified by simulation experiments, and the advantages over existing methods are demonstrated by two empirical examples.
