Stochastic properties of spatial and spatiotemporal ARCH models

  • Philipp OttoEmail author
  • Wolfgang Schmid
  • Robert Garthoff
Regular Article


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.


Moments Probability structure Spatial ARCH Variance clusters 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Leibniz University HannoverHannoverGermany
  2. 2.European University ViadrinaFrankfurt (Oder)Germany

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