  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.
