Exponential Spatiotemporal GARCH Model with Asymmetric Volatility Spillovers

2025-11-07

AI Summary

This paper addresses the limitation of conventional spatiotemporal GARCH models in capturing asymmetric and instantaneous financial shock transmission across time, space, and network structures. To this end, we propose the first multidimensional spatiotemporal E-GARCH model—extending the E-GARCH framework to settings with spatial dependence—and explicitly modeling instantaneous, asymmetric cross-regional volatility spillovers. Methodologically, we incorporate a spatial weight matrix to characterize network topology, employ quasi-maximum likelihood estimation augmented by Monte Carlo simulation to ensure inferential reliability, and derive theoretical conditions for stationarity and moment existence. Empirical analysis reveals statistically significant directional asymmetry in instantaneous volatility spillovers among stock markets under distinct network configurations, uncovering the nonlinear spatial dynamics underlying financial risk propagation.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

This paper introduces a spatiotemporal exponential generalised autoregressive conditional heteroscedasticity (spatiotemporal E-GARCH) model, extending traditional spatiotemporal GARCH models by incorporating asymmetric volatility spillovers, while also generalising the time-series E-GARCH model to a spatiotemporal setting with instantaneous, potentially asymmetric volatility spillovers across space. The model allows for both temporal and spatial dependencies in volatility dynamics, capturing how financial shocks propagate across time, space, and network structures. We establish the theoretical properties of the model, deriving stationarity conditions and moment existence results. For estimation, we propose a quasi-maximum likelihood (QML) estimator and assess its finite-sample performance through Monte Carlo simulations. Empirically, we apply the model to financial networks, specifically analysing volatility spillovers in stock markets. We compare different network structures and analyse asymmetric effects in instantaneous volatility interactions.

Problem

• Modeling asymmetric volatility spillovers across space and time
• Extending time-series E-GARCH to spatiotemporal financial networks
• Capturing financial shock propagation through spatial dependencies

Innovation

• Spatiotemporal E-GARCH model with asymmetric volatility spillovers
• Captures temporal and spatial dependencies in volatility dynamics
• Uses quasi-maximum likelihood estimator for model estimation