Description

“Network Quantile Autoregression (NQAR)” — Härdle, Wang, Wang & Zhu (2017):

1️⃣ The study extends quantile autoregression (Koenker & Xiao, 2006) to networked systems with interdependent nodes.
2️⃣ It models tail risk transmission and herding effects in large financial networks through quantile-dependent dynamics.
3️⃣ The NQAR model introduces node-specific covariates and lagged neighbor effects within a weighted adjacency matrix.
4️⃣ Coefficients ( \beta_0(\tau), \beta_1(\tau), \beta_2(\tau) ) vary across quantiles, capturing asymmetric tail behavior and network feedback.
5️⃣ Estimation uses a minimum contrast method based on asymmetric quantile loss ( \rho_\tau(u) ), ensuring robustness to outliers.
6️⃣ Theoretical results establish stationarity, consistency, and asymptotic normality under high-dimensional network conditions.
7️⃣ Simulations under dyad, block, and power-law topologies show precise coefficient recovery and quantile-dependent impulse responses.
8️⃣ Empirical application to Chinese A-share stocks (2013) reveals strong inter-firm tail linkages and size-driven influence structures.
9️⃣ Impulse-response analysis across τ = 0.05–0.95 uncovers asymmetrical contagion patterns and systemic-risk concentration among SIFIs.
🔟 Conclusion: NQAR unifies quantile dynamics, network topology, and systemic-risk transmission into a coherent econometric framework.