Spatial and spatio-temporal GARCH models

• Applicants: Professor Dr. Philipp Otto; Professor Dr. Wolfgang Schmid
• Subject Area: Statistics and Econometrics
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 412992257

• Final Report Year: 2024

Final Report Abstract

If observations of a random process are spatially or temporally close, they are typically dependent or correlated – a relationship essentially described by Tobler’s First Law of Geography: “Everything is related to everything else, but near things are more related than distant things.” The project focuses on a subfield of spatial statistics, which models this dependence by explicitly incorporating spatial autoregressive terms to explain the dependent variables. This approach plays a significant role in empirical sciences, particularly in spatial econometrics. The topics encompass various phenomena, such as the modelling of air pollution or particulate matter concentrations in the Earth’s atmosphere, property prices, and regional population development. For example, high property prices in one municipality tend to be high in surrounding municipalities as well. In addition to the spatial dependence in the observation values, there is also a spatial dependence in the dispersion of observations and conditional heteroskedasticity. The project aims to develop and expand models for these phenomena. The spatial models are considered analogous to the ARCH (Autoregressive Conditional Heteroskedasticity) model by Robert F. Engle (1982) in time series analysis, for which he was awarded the Nobel Prize in Economics in 2003. Within the project, based on previous work by the applicants introducing the spatial ARCH model, the class of spatial and spatio-temporal GARCH models was introduced. Specifically, logarithmic spatial GARCH models, exponential spatial GARCH models, spatio-temporal GARCH models, and multivariate spatial GARCH models were introduced. Furthermore, stochastic volatility models for spatio-temporal processes were introduced. Immediately following the project, a review paper was written, which systematically structured all spatial and spatiotemporal GARCH processes proposed to date and provided an outlook on possible future research topics.

Publications

• Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity. Spatial Statistics, 26, 125-145.
  Otto, Philipp; Schmid, Wolfgang & Garthoff, Robert
  
• spGARCH: Spatial ARCH and GARCH Models (spGARCH). CRAN: Contributed Packages. The R Foundation.
  Otto, Philipp
  
• Modeling Spatial Dependence in Local Risks and Uncertainties. Proceedings of the 29th European Safety and Reliability Conference (ESREL), 2685-2692. Research Publishing Services.
  Otto, Philipp
  
• spGARCH: An R-Package for Spatial and Spatiotemporal ARCH and GARCH models. The R Journal, 11(2), 401.
  Otto, Philipp
  
• Stochastic properties of spatial and spatiotemporal ARCH models. Statistical Papers, 62(2), 623-638.
  Otto, Philipp; Schmid, Wolfgang & Garthoff, Robert
  
• Directional spatial autoregressive dependence in the conditional first- and second-order moments. Spatial Statistics, 41, 100490.
  Merk, Miryam S. & Otto, Philipp
  
• Online network monitoring. Statistical Methods & Applications, 30(5), 1337-1364.
  Malinovskaya, Anna & Otto, Philipp
  
• A general framework for spatial GARCH models. Statistical Papers, 64(5), 1721-1747.
  Otto, Philipp & Schmid, Wolfgang
  
• Statistical Learning for Change Point and Anomaly Detection in Graphs. Artificial Intelligence, Big Data and Data Science in Statistics, 85-109. Springer International Publishing.
  Malinovskaya, Anna; Otto, Philipp & Peters, Torben
  
• A Dynamic Spatiotemporal Stochastic Volatility Model with an Application to Environmental Risks. Econometrics and Statistics.
  Otto, Philipp; Doğan, Osman & Taşpınar, Süleyman
  
• Dynamic spatiotemporal ARCH models. Spatial Economic Analysis, 19(2), 250-271.
  Otto, Philipp; Doğan, Osman & Taşpınar, Süleyman
  
• Spatial GARCH models for unknown spatial locations – an application to financial stock returns. Spatial Economic Analysis, 19(1), 92-105.
  Fülle, Markus J. & Otto, Philipp
  
• Statistical monitoring of European cross-border physical electricity flows using novel temporal edge network processes
  Malinovskaya, A., Killick, R., Leeming, K. & Otto, P.
  
• Statistical Process Monitoring of Artificial Neural Networks. Technometrics, 66(1), 104-117.
  Malinovskaya, Anna; Mozharovskyi, Pavlo & Otto, Philipp
  
• A multivariate spatial and spatiotemporal ARCH Model. Spatial Statistics, 60, 100823.
  Otto, Philipp
  
• Network log-ARCH models for forecasting stock market volatility. International Journal of Forecasting, 40(4), 1539-1555.
  Mattera, Raffaele & Otto, Philipp
  
• Spatial and spatiotemporal volatility models: A review. Journal of Economic Surveys, 39(3), 1037-1091.
  Otto, Philipp; Doğan, Osman; Taşpınar, Süleyman; Schmid, Wolfgang & Bera, Anil K.
  
• A note on dynamic spatiotemporal ARCH models: small- and large-sample results. AStA Advances in Statistical Analysis, 109(4), 811-828.
  Otto, Philipp; Doğan, Osman & Taşpınar, Süleyman