An extreme value state space model with Gumbel marginals

Eustace, Jayde (2015) An extreme value state space model with Gumbel marginals. Masters thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (846kB)

Abstract

In a 2009 paper, Fougéres, Nolan and Rootzen published an interesting relationship betweeen the Gumbel and exponential stable distributions. The purpose of this research is to explore this relationship and develop a related state space model that can be used to predict and model time dependent processes with Gumbel marginals. Parameter estimation methods will be discussed, both under a simple AR(1) time series with Gumbel marginals and in the context of our proposed state space model. Since our model has a hidden component, we will then discuss filtering methods as well. Gumbel distributed extreme value processes are often found within natural systems, especially in the field of hydrology and in the study of pollution.

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