Direct estimation and inference of differential Granger causality between two high-dimensional time series
arXiv:2109.07609
Abstract
Comparing dependence structures between two related multivariate time series is of fundamental interest in many scientific applications, where changes may occur in both directed temporal interactions and contemporaneous connectivity. Modeling each time series by a vector autoregressive (VAR) model, we propose a new framework for estimation and inference of differential Granger causality (DiffGC) and differential network (DiffNet) structures in high dimensions. The proposed method is based on a novel estimating equation derived from the Yule-Walker equations that directly links the difference between VAR transition matrices to the corresponding difference between precision matrices. Unlike separate estimation strategies that estimate the two VAR models individually and then take their difference, the proposed method directly targets the differential structures and requires sparsity only of the differences, thereby accommodating potentially dense individual networks, including hub structures. Building on the direct estimators, we develop selective inference procedures for both DiffNet and DiffGC parameters, providing valid post-selection inference while accounting for the data-driven screening process. Theoretically, we establish convergence rates and support recovery guarantees for the proposed estimators, derive asymptotic distributions for the selective inference targets, and obtain new consistency results for DiffNet estimation under weaker assumptions than existing methods. Simulation studies confirm the theoretical convergence rates and demonstrate accurate support recovery and robust inferential performance. An application to resting-state electroencephalography (EEG) data identifies substantial changes in both contemporaneous and Granger-causal connectivity across recording sessions.
56 pages; 7 figures