Nonlinear dependence in time series, spatial models and spatio-temporal models

The aim of the project is to study nonlinear dependence, both in theory and in applications. Corresponding to the area of application the project has been split into 4 sub-pojects. a) Nonlinear dependence in time series The goal is to improve and extend the very recent theory of nonparametric regression on a nonstationary regressor, and to exploit this in working on the problem of nonlinear cointegration. The plan is to start with a simple joint threshold model and then extend this in stages. b) Nonlin ear dependence in spatial models Additive approximation is proposed as a new tool in characterizing nonlinear (auto) dependence for a spatial varaiable. Two publications are in progress using different methods of estimating the additive approximation. Fur ther work is planned to include test of linearity, estimating the order in the various directions, and testing for isotropy. All of this will be applied to analysis of spatial textures. c) Nonlinear dependence in spatio-temporal models In geophysics lin ear techniques such as EOF (principal components) have dominated. Alternative methods based on independent components have recently been introduced. The idea is to take advantage of these techniques and combine them with the additive spatial approximation developed under b). There are challenges from a theoretical point of view in establishing properties of estimates of independent components and from an applied point of view in applying the new methods to meteorological and climatological data. d) Class es of nonlinear dependence measures This is partly a new research topic to me. The goal is to extend the local dependence measures, which have the important property of having a direction, to a multivariate framework and to apply these in particular to t he problems outlined in parts b) and c).