Environmental and Ecological Statistics

, Volume 14, Issue 3, pp 285–299 | Cite as

Time-varying models for extreme values



We propose a new approach for modeling extreme values that are measured in time and space. First we assume that the observations follow a Generalized Extreme Value (GEV) distribution for which the location, scale or shape parameters define the space–time structure. The temporal component is defined through a Dynamic Linear Model (DLM) or state space representation that allows to estimate the trend or seasonality of the data in time. The spatial element is imposed through the evolution matrix of the DLM where we adopt a process convolution form. We show how to produce temporal and spatial estimates of our model via customized Markov Chain Monte Carlo (MCMC) simulation. We illustrate our methodology with extreme values of ozone levels produced daily in the metropolitan area of Mexico City and with rainfall extremes measured at the Caribbean coast of Venezuela.


Spatio-temporal process Extreme values GEV distribution Process convolutions MCMC Ozone levels 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA
  2. 2.Department of Applied Mathematics and StatisticsUniversity of CaliforniaSanta CruzUSA

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