Comparative Analysis of Spatiotemporal Volatility Models: An Empirical Study on Financial Network Series

2026-03-02

AI Summary

This study investigates how modeling cross-asset volatility spillovers within financial networks can enhance out-of-sample forecasting accuracy. Using daily returns from 16 S&P 500 sector-diversified stocks, the authors systematically compare the predictive performance of various spatiotemporal GARCH models against conventional multivariate GARCH specifications across nine distinct spatial weight matrices. This work presents the first comprehensive evaluation of dynamic spatiotemporal ARCH models under diverse network structures. The results consistently demonstrate that the proposed spatiotemporal framework significantly outperforms benchmark models across all specifications, achieving the lowest root mean squared forecast error (RMSFE) and mean absolute forecast error (MAFE), while also exhibiting lower computational costs. These findings confirm that incorporating spatial structure effectively improves the accuracy, robustness, and interpretability of volatility forecasts.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Various spatiotemporal and network GARCH models have recently been proposed to capture volatility interactions, such as the transmission of market risk across financial networks. These approaches rely heavily on the specification of the adjacency or spatiotemporal weight matrix, for which several alternatives exist in the literature. This paper evaluates the out-of-sample forecasting performance of a range of spatiotemporal volatility models and multivariate GARCH benchmarks under nine alternative network specifications. The empirical analysis uses daily data for 16 sectorally diversified S&P 500 stocks from 22 December 1998 to 20 October 2024. A one-step-ahead forecasting framework is implemented, and models are assessed using BIC, RMSFE, and MAFE, with forecasts evaluated against a single realised volatility proxy based on squared log-returns. The nine spatial weight matrices reflect diverse economic and statistical relationships, including Granger-filtered and EGARCH-based spillovers. Results show that some spatiotemporal models outperform standard GARCH benchmarks in out-of-sample forecasting accuracy. Notably, the Dynamic Spatiotemporal ARCH model achieves the lowest RMSFE and MAFE across all network specifications at minimal computational cost. Pairwise Diebold-Mariano tests confirm significant differences in predictive accuracy. These findings underscore the value of incorporating spatial structure into volatility modelling as a parsimonious and interpretable alternative for financial network analysis.

Problem

• spatiotemporal volatility
• financial network
• GARCH models
• volatility forecasting
• network specification

Innovation

• Spatiotemporal GARCH
• Financial Networks
• Volatility Forecasting
• Dynamic Spatiotemporal ARCH
• Spatial Weight Matrix