Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/311916 
Year of Publication: 
2022
Citation: 
[Journal:] Statistical Papers [ISSN:] 1613-9798 [Volume:] 64 [Issue:] 5 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 1721-1747
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
In time-series analysis, particularly in finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased risk). In contrast, it has not been considered to be of critical importance until now to model spatial dependence in the conditional second moments. Only a few models have been proposed for modelling local clusters of increased risks. In this paper, we introduce a novel spatial GARCH process in a unified spatial and spatiotemporal GARCH framework, which also covers all previously proposed spatial ARCH models, exponential spatial GARCH, and time-series GARCH models. In contrast to previous spatiotemporal and time series models, this spatial GARCH allows for instantaneous spill-overs across all spatial units. For this common modelling framework, estimators are derived based on a non-linear least-squares approach. Eventually, the use of the model is demonstrated by a Monte Carlo simulation study and by an empirical example that focuses on real estate prices from 1995 to 2014 across the postal code areas of Berlin. A spatial autoregressive model is applied to the data to illustrate how locally varying model uncertainties (e.g., due to latent regressors) can be captured by the spatial GARCH-type models.
Subjects: 
Spatial GARCH
Spatiotemporal statistics
Volatility clusters
Real estate prices
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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