Regularized Estimation in High-Dimensional Vector Auto-Regressive Models Using Spatio-Temporal Information

Zhenzhong Wang, Abolfazl Safikhani, Zhengyuan Zhu, David S. Matteson
2023 Statistica sinica  
The Vector Auto-Regressive (VAR) model is commonly used to model multivariate time series, and there are many penalized methods to handle high dimensionality. However in terms of spatio-temporal data, most methods do not take the spatial and temporal structure of the data into consideration, which may lead to unreliable network detection and inaccurate forecasts. This paper proposes a data-driven weighted l1 regularized approach for spatio-temporal VAR model. Extensive simulation studies are
more » ... ried out to compare the proposed method with five existing methods of high-dimensional VAR model, demonstrating improvements of our method over others in parameter estimation, network detection and out-of-sample forecasts. We also apply our method on a traffic data set to evaluate its performance in real application. In addition, we explore the theoretical properties of l1 regularized estimation of VAR model under the weakly sparse scenario, in which the exact sparsity can be viewed as a special case. To the best of our knowledge, this direction has not been considered yet in the literature. For general stationary VAR process, we derive the non-asymptotic upper bounds on l1 regularized estimation errors, provide the conditions of es-
doi:10.5705/ss.202020.0056 fatcat:sq6gamtyendnjhahmepqwv7nv4