Spatial Long-Range Dependence

Long memory is a well-known and often observed statistical properties of time series. A process is called to have long memory, if the temporal autocorrelation is rather slowly decreasing, e.g. compared to autoregressive processes. There are many statistical models accounting for such long memory. In spatial statistics, however, there are just a few attempts to model long-range dependencies. Previous approaches of long-range/memory dependence models for spatial models have mostly focussed on geostatistical settings. In contrast to the spatial econometrics’ framework, where the spatial dependence is modelled via a suitable spatial weights matrix, which defines the extend of the correlation to all adjacent regions, geostatistical approaches capture the spatial dependence by a proper choice of the covariance matrix of a multivariate process. The entries of this covariance matrix usually follows a certain parametric covariance function depending on the difference between two locations. Two-dimensional spatial lattice data has been considered, where the spatial dependence is separable. For this master thesis, the current literature on spatial long-range dependence and spatial long memory should be reviewed. Moreover, previously proposed methods could be applied to real or artificial/simulated data, but there should not necessarily be an empirical part in this master thesis. Alternatively, a quantitative/systematic literature review can be conducted.

Requirements

1. Interest in the statistical analysis

2. Affinity to work with the academic literature

3. Good writing skills

Contact

Prof. Dr. Philipp Otto (philipp.otto@ikg.uni-hannover.de)

Anna Malinovskaya (anna.malinovskaya@ikg.uni-hannover.de)