TY - JOUR

T1 - Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity

AU - Otto, Philipp

AU - Schmid, Wolfgang

PY - 2016/9/2

Y1 - 2016/9/2

N2 - 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.

AB - 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.

KW - Lung cancer mortality

KW - SARspARCH

KW - Spatial ARCH

KW - Variance clusters

UR - http://www.scopus.com/inward/record.url?scp=85050855931&partnerID=8YFLogxK

U2 - 10.1016/j.spasta.2018.07.005

DO - 10.1016/j.spasta.2018.07.005

M3 - Article

VL - 26

SP - 125

EP - 145

JO - Spatial Statistics

JF - Spatial Statistics

SN - 2211-6753

ER -