A1401
Title: Local interaction autoregressive model for high dimension time series data
Authors: Jingyang Li - University of Michigan (United States) [presenting]
Yang Chen - University of Michigan (United States)
Abstract: High-dimensional matrix- and tensor-valued time series arise in fields such as economics, geophysics, and environmental science. Traditional vector autoregressive models are infeasible in these settings due to excessive parameters and loss of spatial structure under vectorization. Existing matrix autoregressive (MAR) models also face two limitations: They assume each location depends on the entire spatial field from the previous step, while in practice, local interactions dominate; and they impose restrictive low-dimensional structures on the coefficient matrices, limiting flexibility in capturing heterogeneous dependencies. A local interaction autoregressive (LIAR) model is proposed that incorporates spatial locality into matrix and tensor autoregression. Each entry depends only on a neighborhood in past observations, with neighborhoods allowed to vary across locations. A parallel least squares estimator is developed with closed-form solutions for efficient large-scale computation. To further reduce complexity, a separable variant, SP-LIAR, is introduced which preserves flexibility with fewer parameters. Asymptotic theory is established, including consistency, asymptotic normality, and consistent neighborhood selection under broad regimes. Simulations and real data applications show that LIAR offers an effective balance of interpretability, flexibility, and computational efficiency.
