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Title: Spatial GARCH-type models: A unified approach Authors:  Philipp Otto - Leibniz University Hannover (Germany) [presenting]
Wolfgang Schmid - European University Viadrina (Germany)
Abstract: In time series analysis and, particularly, in finance, (generalized) autoregressive conditional heteroscedasticity models are widely applied statistical tools for modelling volatility clusters, i.e., periods of increased or decreased risks. In contrast, spatial dependence in the conditional second moments of spatial and spatiotemporal processes has been seen rather uncritical up to now. There are only a few models, which have been proposed for modelling local clusters of increased risks. We introduce a unified spatial and spatiotemporal GARCH-type model, which covers all previously proposed spatial ARCH models but also introduces novel spatial GARCH as well as E-GARCH processes. For this common modelling framework, maximum-likelihood estimators are derived. In addition to the theoretical contributions, we suggest a model selection strategy verified by a series of Monte-Carlo simulation studies. Eventually, the use of the unified model is demonstrated by an empirical example. In particular, we focus on real-estate prices from 1995 to 2014 in all Berlin ZIP code areas. For these data, a spatial autoregressive model has been applied, which shows locally varying model uncertainties captured by the spatial GARCH-type models.