2014/08/02 by Cho, Yongbum, Davis, Richard A., Ghosh, Souvik · 1 citation
#FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1408.0412
The extremogram, proposed by Davis and Mikosch (2008), is a useful tool for measuring extremal dependence and checking model adequacy in a time series. We define the extremogram in the spatial domain when the data is observed on a lattice or at locations distributed as a Poisson point process in d-dimensional space. Under mixing and other conditions, we establish a central limit theorem for the empirical spatial extremogram. We show these conditions are applicable for max-moving average processes and Brown-Resnick processes and illustrate the empirical extremogram's performance via simulation. We also demonstrate its practical use with a data set related to rainfall in a region in Florida.