Abstract
Each of the extreme value models derived so far has been obtained through mathematical arguments that assume an underlying process consisting of a sequence of independent random variables. However, for the types of data to which extreme value models are commonly applied, temporal independence is usually an unrealistic assumption. In particular, extreme conditions often persist over several consecutive observations, bringing into question the appropriateness of models such as the GEV. A detailed investigation of this question requires a mathematical treatment at a greater level of sophistication than we have adopted so far. However, the basic ideas are not difficult and the main result has a simple heuristic interpretation. A more precise development is given by Leadbetter et al. (1983).
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Further Reading
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Coles, S. (2001). Extremes of Dependent Sequences. In: An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics. Springer, London. https://doi.org/10.1007/978-1-4471-3675-0_5
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DOI: https://doi.org/10.1007/978-1-4471-3675-0_5
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