Two-way Homogeneity Pursuit for Quantile Network Vector Autoregression

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.