A0931
Title: Sufficient dimension reduction for high-dimensional nonlinear vector autoregressive models
Authors: Jiaying Weng - Bentley University (United States) [presenting]
S Yaser Samadi - Southern Illinois University Carbondale (United States)
Abstract: Vector autoregressive (VAR) models are fundamental tools for analyzing multivariate time series data across diverse domains. However, modeling high-dimensional time series data poses challenges due to the curse of dimensionality, especially when incorporating multiple time series and escalating model complexity. Sufficient dimension reduction (SDR) is a concept in statistics and machine learning aimed at finding a lower-dimensional subspace of the original feature space that preserves the relevant information for the target variable(s) or response variable(s). The SDR is explored in nonlinear vector autoregressive (NVAR) models, where the current state depends on multiple indices defined in past lags with an unknown relationship. A novel time series martingale difference divergence matrix (MDDM) approach is proposed, tailored for non-sparse estimation, albeit suitable only for low-dimensional scenarios. However, in the context of high-dimensional complexities where the dimensions grow rapidly by increasing the size of series and lag order, a sparse estimation procedure is designed within the proposed MDDM method, leveraging a regularized optimization framework equipped with the LASSO penalty. Theoretical foundations are rigorously presented for both non-sparse and sparse estimators. Through simulations and real data analyses, the efficacy of the methodology in handling high-dimensional time series data is demonstrated within NVAR frameworks.
