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A Multivariate Spatial and Spatiotemporal ARCH Model

Philipp Otto

arXiv 26 Apr 2022 · Statistics — Methodology · publishedSpatial Statistics (2024) · 3 citations (OpenAlex)

arXiv:2204.12472 · PDF · DOI · OpenAlex · Extracted main text

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 in the conditional variance, as they are usually present in spatial econometric applications. Furthermore, spatial and temporal cross-variable effects 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 spill-overs.

Citation extraction

26
references
46
in-text mentions
26
distinct cited
4
self-citations
6,149
main-text words

appendix boundary found by appendix_titled_section at “Appendix” · 68% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Yang, K. and Lee, L.-f (2017) Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models0.9619389%
2Otto, P. and Schmid, W (2019) Spatial and spatiotemporal GARCH models – a unified approach self0.87452100%
3Otto, P., Schmid, W., and Garthoff, R (2018) Generalised Spatial and Spatiotemporal Autoregressive Conditional Heteroscedasticity self0.73732100%
4Yu, J., de Jong, R., and Lee, L.-f (2008) Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large0.73732100%
5Borovkova, S. and Lopuhaa, R (2012) Spatial GARCH: A spatial approach to multivariate volatility modeling0.64422100%
6Engle, R. F. and Kroner, K. F (1995) Multivariate simultaneous generalized ARCH0.64422100%
7Sato, T. and Matsuda, Y (2021) Spatial extension of generalized autoregressive conditional heteroskedasticity models0.64422100%
8Francq, C. and Zakoian, J.-M (2011) GARCH models: Structure, Statistical Inference and Financial Applications0.51121100%
9Bollerslev, T (1986) Generalized autoregressive conditional heteroskedasticity0.40511100%
10Brockwell, P. J. and Davis, R. A (2006) Introduction to time series and forecasting0.40511100%

Showing the top 10 of 26 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Spatiotemporal Autoregressive Models for Areal Compositional Data0.64422
2Spatial and Spatiotemporal Volatility Models: A Review0.51121
3A Dynamic Spatiotemporal and Network ARCH Model with Common Factors0.40511