Neighborhood VAR: Efficient estimation of multivariate timeseries with neighborhood information

Abstract

Vector autoregression (VAR) models are popular in modeling multivariate time series in data sciences and other areas. When the number of time series is large, the number of parameters in the VAR model increases dramatically, posing great challenges for proper model estimation and inference. In this work, we propose a so-called neighborhood vector autoregression (NVAR) model to efficiently analyze large-dimensional multivariate time series. We assume that the time series have underlying neighborhood relationships, e.g., spatial or network, among them based on the inherent setting of the problem. When this neighborhood information is available or can be summarized using a distance matrix, we demonstrate that our proposed NVAR method provides a computationally efficient and theoretically sound estimation of model parameters. The performance of the proposed method is compared with other existing approaches in both simulation studies and a real-data application in environmental science.