Two-way Homogeneity Pursuit for Quantile Network Vector Autoregression

TL;DR

This paper introduces a novel two-way grouped network quantile autoregression model for high-dimensional time series on large-scale networks, enabling simultaneous node clustering and model estimation with theoretical guarantees.

Contribution

It develops a new quantile VAR model that accounts for directional network interactions, with consistent estimation of node groups and parameters, and a criterion for selecting the number of groups.

Findings

Consistent estimation of node group memberships and model parameters.

Asymptotic normality of estimated parameters under correct group specification.

Effective model selection via a new quantile information criterion.

Abstract

While the Vector Autoregression (VAR) model has received extensive attention for modelling complex time series, quantile VAR analysis remains relatively underexplored for high-dimensional time series data. To address this disparity, we introduce a two-way grouped network quantile (TGNQ) autoregression model for time series collected on large-scale networks, known for their significant heterogeneous and directional interactions among nodes. Our proposed model simultaneously conducts node clustering and model estimation to balance complexity and interpretability. To account for the directional influence among network nodes, each network node is assigned two latent group memberships that can be consistently estimated using our proposed estimation procedure. Theoretical analysis demonstrates the consistency of membership and parameter estimators even with an overspecified number of groups. With the correct group specification, estimated parameters are proven to be asymptotically normal, enabling valid statistical inferences. Moreover, we propose a quantile information criterion for consistently selecting the number of groups. Simulation studies show promising finite sample performance, and we apply the methodology to analyze connectedness and risk spillover effects among Chinese A-share stocks.