A general framework for spatial GARCH models

Otto, P. and Schmid, W. (2022) A general framework for spatial GARCH models. Statistical Papers, (doi: 10.1007/s00362-022-01357-1) (Early Online Publication)

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.

• Item Type: Articles
• Additional Information: Open Access funding enabled and organized by Projekt DEAL. Funding was provided by Deutsche Forschungsgemeinschaft (Grant No. 412992257).
• Status: Early Online Publication
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Otto, Dr Philipp
• Authors: Otto, P., and Schmid, W.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Statistical Papers
• Publisher: Springer
• ISSN: 0932-5026
• ISSN (Online): 1613-9798
• Published Online: 29 September 2022
• Copyright Holders: Copyright © The Author(s) 2022
• First Published: First published in Statistical Papers 2023
• Publisher Policy: Reproduced under a Creative Commons license