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Generalised least squares estimation of regularly varying space-time processes based on flexible observation schemes

  • Sven Buhl
  • Claudia Klüppelberg


Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such stationary processes we propose a two-step parameter estimation of the extremogram, when some part of the domain of interest is fixed and another increasing. We provide conditions for consistency and asymptotic normality of the empirical extremogram centred by a pre-asymptotic version for such observation schemes. For max-stable processes with Fréchet margins we provide conditions, such that the empirical extremogram (or a bias-corrected version) centred by its true version is asymptotically normal. In a second step, for a parametric extremogram model, we fit the parameters by generalised least squares estimation and prove consistency and asymptotic normality of the estimates. We propose subsampling procedures to obtain asymptotically correct confidence intervals. Finally, we apply our results to a variety of Brown-Resnick processes. A simulation study shows that the procedure works well also for moderate sample sizes.


Brown-Resnick process Extremogram Generalised least squares estimation Max-stable process Observation schemes Regularly varying process Semiparametric estimation Space-time process 

AMS 2000 Subject Classifications

Primary: 60F05 60G70 62F12 62G32 Secondary: 37A25 62M30 62P12 


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Sven Buhl acknowledges support by the Deutsche Forschungsgemeinschaft (DFG) through the TUM International Graduate School of Science and Engineering (IGSSE).


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Authors and Affiliations

  1. 1.Center for Mathematical SciencesTechnical University of MunichGarchingGermany

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