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A multivariate spatial and spatiotemporal ARCH model

Otto, P. (2024) A multivariate spatial and spatiotemporal ARCH model. Spatial Statistics, 60, 100823. (doi: 10.1016/j.spasta.2024.100823)

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Abstract

This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects, as they are usually present in geo-referenced data. Furthermore, spatial and temporal cross-variable effects in the conditional variance are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous) spatial interactions, while the temporal autoregressive structure in the market risks is of higher importance. Interactions between the different property types only occur in the temporally lagged variables. Thus, we see mainly temporal volatility clusters and weak spatial volatility spillovers.

Item Type:Articles
Additional Information:Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — 501539976.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Otto, Dr Philipp
Authors: Otto, P.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Spatial Statistics
Publisher:Elsevier
ISSN:2211-6753
ISSN (Online):2211-6753
Published Online:02 April 2024
Copyright Holders:Copyright © 2024 The Author
First Published:First published in Spatial Statistics 60:100823
Publisher Policy:Reproduced under a Creative Commons License

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