Stochastic properties of spatial and spatiotemporal ARCH models

Philipp Otto (), Wolfgang Schmid and Robert Garthoff
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Philipp Otto: Leibniz University Hannover
Wolfgang Schmid: European University Viadrina
Robert Garthoff: European University Viadrina

Statistical Papers, 2021, vol. 62, issue 2, No 3, 623-638

Abstract: Abstract In this paper, we provide some results on the class of spatial autoregressive conditional heteroscedasticity (ARCH) models, which have been introduced in recent literature to model spatial conditional heteroscedasticity. That means that the variance in some locations depends on the variance in neighboring locations. In contrast to the temporal ARCH model, for which the distribution is known, given the full information set for the prior periods, the distribution is not straightforward in the spatial and spatiotemporal settings. Thus, we focus on the probability structure of these models. In particular, we derive the conditional and unconditional moments of the process as well as the distribution of the process, given a known error distribution. Eventually, it is shown that the process is strictly stationary under certain conditions.

Keywords: Moments; Probability structure; Spatial ARCH; Variance clusters (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-019-01106-x

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