Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity

Philipp Otto; Wolfgang Schmid

doi:10.1016/j.spasta.2018.07.005

Details

Original language	English
Pages (from-to)	125-145
Number of pages	21
Journal	Spatial Statistics
Volume	26
Publication status	Published - 2 Sept 2016
Externally published	Yes

Abstract

In this paper, we introduce a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional heteroscedasticity (ARCH) model. We show additionally how the introduced spatial ARCH model can be used in spatiotemporal settings. In contrast to the temporal ARCH model, in which the distribution is known given the full information set of the prior periods, the distribution is not straightforward in the spatial and spatiotemporal setting. However, it is possible to estimate the parameters of the model using the maximum-likelihood approach. Via Monte Carlo simulations, we demonstrate the performance of the estimator for a specific spatial weighting matrix. Moreover, we combine the known spatial autoregressive model with the spatial ARCH model assuming heteroscedastic errors. Eventually, the proposed autoregressive process is illustrated using an empirical example. Specifically, we model lung cancer mortality in 3108 U. S. counties and compare the introduced model with two benchmark approaches.

Keywords

Lung cancer mortality, SARspARCH, Spatial ARCH, Variance clusters

ASJC Scopus subject areas

Earth and Planetary Sciences(all)
Computers in Earth Sciences
Environmental Science(all)
Management, Monitoring, Policy and Law
Mathematics(all)
Statistics and Probability

Sustainable Development Goals

SDG 3 - Good Health and Well-being

Cite this

Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity. / Otto, Philipp; Schmid, Wolfgang.
In: Spatial Statistics, Vol. 26, 02.09.2016, p. 125-145.

Research output: Contribution to journal › Article › Research › peer review

Otto, P & Schmid, W 2016, 'Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity', Spatial Statistics, vol. 26, pp. 125-145. https://doi.org/10.1016/j.spasta.2018.07.005

Otto, P., & Schmid, W. (2016). Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity. Spatial Statistics, 26, 125-145. https://doi.org/10.1016/j.spasta.2018.07.005

Otto P, Schmid W. Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity. Spatial Statistics. 2016 Sept 2;26:125-145. doi: 10.1016/j.spasta.2018.07.005

Otto, Philipp ; Schmid, Wolfgang. / Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity. In: Spatial Statistics. 2016 ; Vol. 26. pp. 125-145.

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Research@Leibniz University