Spatial and spatio-temporal GARCH models

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The project aims to develop new models in spatial statistics, which deals with the analysis of random processes in space. Such processes are highly important in empirical research and particularly in econometrics. For instance, spatial statistics covers the analysis of processes on the surface of the Earth or the atmosphere, like air pollutants and particulate matters, regional prices for building land, or the population in municipalities. Generally, one can observe that observations, which are close together in space, are more similar than observations that are more distant in space; e.g., if the prices for building land are high in one municipality, then one might expect high prices in the neighboring municipalities. This phenomenon can be modeled by spatial autoregressive processes.Beside this spatial dependence of the observed values, an analog dependence can be observed for the variation of the data and the conditional heteroscedasticity. In this project, statistical models should be developed for data showing this behavior. In particular, the spatial model is defined in an analogous manner to the time-series ARCH model invented by Robert F. Engle (1982), who won the Nobel Memorial Prize in Economics for this theory in 2003.In addition, a multivariate spatial ARCH model should be introduced, such that several statistical variables can be modeled simultaneously, like for instance, several environmental pollutants and particulate matters. For this example, the spatial dependence is influenced by the wind direction and speed, which are in fact stochastic variables. Thus, a further aspect of the project is the analysis of stochastic spatial dependence and weighting schemes.