Paper: arXiv 2508.20101

Authors: Atika Aouri, Philipp Otto

Abstract

We introduce a heterogeneous spatiotemporal GARCH model for geostatistical data or processes on networks, e.g., for modelling and predicting financial return volatility across firms in a latent spatial framework. The model combines classical GARCH(p, q) dynamics with spatially correlated innovations and spatially varying parameters, estimated using local likelihood methods. Spatial dependence is introduced through a geostatistical covariance structure on the innovation process, capturing contemporaneous cross-sectional correlation. This dependence propagates into the volatility dynamics via the recursive GARCH structure, allowing the model to reflect spatial spillovers and contagion effects in a parsimonious and interpretable way. In addition, this modelling framework allows for spatial volatility predictions at unobserved locations. In an empirical application, we demonstrate how the model can be applied to financial stock networks. Unlike other spatial GARCH models, our framework does not rely on a fixed adjacency matrix; instead, spatial proximity is defined in a proxy space constructed from balance sheet characteristics. Using daily log returns of 50 publicly listed firms over a one-year period, we evaluate the model’s predictive performance in a cross-validation study.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a highly advanced spatiotemporal GARCH model with spatially varying parameters, geostatistical covariance structures, and a latent economic space, requiring advanced stochastic calculus and local likelihood estimation. While it includes a cross-validation study, it is limited to a single year of data for only 50 firms, lacks implementation details for backtesting, and does not report robust performance metrics like those needed for production-ready strategies.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Model & Predict Volatility in Financial Networks"] --> B["Data Input:<br>Daily log returns of 50 firms over 1 year"]
  B --> C["Methodology:<br>Heterogeneous Spatiotemporal GARCH Model"]
  C --> D["Computational Process:<br>Local Likelihood Estimation"]
  D --> E["Key Outcome 1:<br>Spatial volatility predictions at unobserved locations"]
  D --> F["Key Outcome 2:<br>Parsimonious spatial spillover & contagion effects"]
  E --> G["Validation:<br>Cross-validation study"]
  F --> G

Cited References (32)

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  6. Mat 'e rn cross-covariance functions for multivariate random fields (2010)
  7. Dynamic spatiotemporal ARCH models (2024)
  8. Spatial GARCH : A spatial approach to multivariate volatility modeling (2012)
and 24 more
  1. Networks in risk spillovers: A multivariate GARCH perspective (2023)
  2. Proximity-structured multivariate volatility models (2015)
  3. Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity (2018)
  4. Scenario analysis of livestock-related PM2.5 pollution based on a new heteroskedastic spatiotemporal model (2024)
  5. A dynamic spatiotemporal stochastic volatility model with an application to environmental risks (2023)
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1 of 32 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.