Network Vector Autoregression

30 Pages Posted: 13 May 2016

See all articles by Xuening Zhu

Xuening Zhu

Peking University

Rui Pan

Peking University

Guodong Li

The University of Hong Kong - Department of Statistics and Actuarial Science

Yuewen Liu

Xi'an Jiaotong University

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: May 11, 2016

Abstract

We consider here a large-scale social network with a continuous response observed for each node at equally spaced time points. The responses from different nodes constitute an ultra-high dimensional vector, whose time series dynamic is to be investigated. In addition, the network structure is also taken into consideration, for which we propose a network vector autoregressive (NAR) model. The NAR model assumes each node's response at a given time point as a linear combination of (a) its previous value, (b) the average of its connected neighbors, (c) a set of node-specific covariates, and (d) an independent noise. The corresponding coeffcients are referred to as the momentum effect, the network effect, and the nodal effect respectively. Conditions for strict stationarity of the NAR models are obtained. In order to estimate the NAR model, an ordinary least squares type estimator is developed, and its asymptotic properties are investigated. We further illustrate the usefulness of the NAR model through a number of interesting potential applications. Simulation studies and an empirical example are presented.

Keywords: multivariate time series, ordinary least squares, social network, vector autoregression

JEL Classification: C30

Suggested Citation

Zhu, Xuening and Pan, Rui and Li, Guodong and Liu, Yuewen and Wang, Hansheng, Network Vector Autoregression (May 11, 2016). Available at SSRN: https://ssrn.com/abstract=2778874 or http://dx.doi.org/10.2139/ssrn.2778874

Xuening Zhu

Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Rui Pan

Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Guodong Li

The University of Hong Kong - Department of Statistics and Actuarial Science ( email )

Pokfulam Road
Hong Kong
China

Yuewen Liu

Xi'an Jiaotong University ( email )

28,Xianning West Road
Xi'an, Shaanxi 710049
China

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

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