Spatial Dependence and Space-Time Trend in Extreme Events

John Einmahl, Ana Ferreira, Laurens de Haan, C. Neves, C. Zhou

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The statistical theory of extremes is extended to observations that are non-stationary and not indepen- dent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations, taken over time and space. The results yield two statistical tests for homoscedastic- ity in the tail, one in space and one in time. Further, we show that the common extreme value index can be estimated via a pseudo-maximum likelihood procedure based on pooling all (non-stationary and dependent) observations. Our leading example and application is rainfall in Northern Germany.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages25
Publication statusPublished - 24 Mar 2020

Publication series

NameCentER Discussion Paper


  • Multivariate extreme value statistics
  • non-identical distributions
  • sequential tail empirical process
  • testing


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