Network Vector Autoregression

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 coefficients 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.

Estimation and model selection in general spatial dynamic panel data models

“…Moran's I statistics (19) and P values under the null hypothesis of no spatial correlation between y (1) i,t and y (2) i,t at each time t, which are calculated using the spatial weight matrix Wn = D −1 A, where A = (aij ) is the queen contiguity matrix chosen by following ref. 1, and D = diag( n j =1 a1j , n j =1 a2j , .…”

“…If we can effectively model where and when crime occurs, we can launch better preventative measures. As another example, data collected from Sina Weibo, the largest Twitter-like social network in China, can be better modeled if one leverages user-specific covariates and information about the network structure; good modeling allows us to detect key players in the network, and this knowledge can be used to improve targeted marketing (2). More examples can be found in the literature; e.g., ref.…”

Network Influence Analysis

“…For the sake of completeness, define a jj = 0 for any 1 ≤ j ≤ n. Accordingly, the matrix A = (a ij ) n×n ∈ R n×n with i, j = 1, • • • , n, describes the network relationships among the n nodes. In social network studies, A is called the adjacency matrix and presents useful information relating any two adjacent nodes (see, e.g., Zhu et al, 2017;Zou et al, 2017). For node i, let Y i be its associated response variable.…”

Dynamic Influence Prediction of Social Network Based on Partial Autoregression Single Index Model

“…Meanwhile, we focus on the nodal influence predication of social network. The current frontier is the Network Vector Autoregression (NAR) model (Zhu, 2017) [17], which made use of a linear regression approach synthesizing time series dynamics and network structure. However, it is hard for such a linear model to fit complex and volatile configuration all the time.…”