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Extreme Value Time Series

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Climate Time Series Analysis

Part of the book series: Atmospheric and Oceanographic Sciences Library ((ATSL,volume 51))

Abstract

Extreme value time series refer to the outlier component in the climate equation (Eq. 1.2). Quantifying the tail probability of the PDF of a climate variable—the risk of climate extremes—is of high socioeconomical relevance. In the context of climate change, it is important to move from stationary to nonstationary (time-dependent) models: with climate changes also risk changes may be associated.

Traditionally, extreme value data are evaluated in two forms: first, block extremes such as annual maxima, and, second, exceedances of a high threshold. A stationary model of great flexibility for the first and the second form is the Generalized Extreme Value distribution and the generalized Pareto distribution, respectively. Classical estimation techniques based on maximum likelihood exist for both distributions.

Nonstationary models can be constructed parametrically, by writing the extreme value models with time-dependent parameters. Maximum likelihood estimation may impose numerical challenges here. The inhomogeneous Poisson process constitutes an interesting nonparametric model of the time-dependence of the occurrence of an extreme. Here, bootstrap confidence bands can be constructed and hypothesis tests performed to assess the significance of trends in climate risk. A recent development is a hybrid, which estimates the time-dependence nonparametrically and, conditional on the occurrence of an extreme, models the extreme value parametrically.

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    Manfred Mudelsee

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Mudelsee, M. (2014). Extreme Value Time Series. In: Climate Time Series Analysis. Atmospheric and Oceanographic Sciences Library, vol 51. Springer, Cham. https://doi.org/10.1007/978-3-319-04450-7_6

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