View Submission - COMPSTAT2018

A0416
**Title: **Spatial and spatiotemporal ARCH-type models
**Authors: **Philipp Otto - Leibniz University Hannover (Germany) **[presenting]**

**Abstract: **A general overview on spatial and spatiotemporal ARCH models is provided. To define spatial models, in particular areal spatial models like simultaneous autoregressive (SAR) models, it is convenient to consider a vector of observations $Y = (Y(s_1), \ldots, Y(s_n))^\prime$ at all locations $s_1, \ldots, s_n$. For spatial ARCH models, we specify this vector as $Y = \mathrm{diag}(h)^{1/2} {\varepsilon}$, analogue to the well-known time series ARCH models. However, note that the vector $h = (h(s_1), \ldots, h(s_n))^\prime$ does not necessarily coincide with the conditional variance $Var(Y( {s}_i) | Y(s_1), \ldots, Y(s_{i-1}))$, as the variance in any location $s_j$ for $j \neq i$ also depends on $Y(s_i)$. We now distinguish between several spatial ARCH-type models via the definition of $h$. In particular, we distinguish between three different spatial ARCH-type models. Beside the original definition, we introduce an exponential spatial ARCH model and propose maximum-likelihood estimators for the parameters of this new model. In addition, we consider a complex-valued definition of the spatial ARCH. From a practical point of view, the use of the R-package spGARCH is demonstrated.