Neighborhood VAR: Efficient estimation of multivariate timeseries with neighborhood information

TL;DR

This paper introduces Neighborhood VAR, a computationally efficient method for estimating large multivariate time series models by leveraging neighborhood information, applicable in environmental and network data contexts.

Contribution

The paper proposes a novel NVAR model that incorporates neighborhood relationships to improve efficiency and scalability in multivariate time series analysis.

Findings

NVAR outperforms existing methods in simulations.

NVAR effectively models spatial and network dependencies.

Application to stream nitrogen data demonstrates practical utility.

Abstract

In data science, vector autoregression (VAR) models are popular in modeling multivariate time series in the environmental sciences and other applications. However, these models are computationally complex with the number of parameters scaling quadratically with the number of time series. 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 application of stream nitrogen study.