Abstract
This paper presents applications of the peaks-over-threshold methodology for both the univariate and the recently introduced bivariate case, combined with a novel bootstrap approach. We compare the proposed bootstrap methods to the more traditional profile likelihood. We have investigated 63 years of the European Climate Assessment daily precipitation data for five Hungarian grid points, first separately for the summer and winter months, then aiming at the detection of possible changes by investigating 20 years moving windows. We show that significant changes can be observed both in the univariate and the bivariate cases, the most recent period being the most dangerous in several cases, as some return values have increased substantially. We illustrate these effects by bivariate coverage regions.
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Notes
The (old) parameter σ in terms of ξ and H −1(q): \(\sigma = \sigma (\xi ,H^{-1}(q)) =\frac {\xi H^{-1}(q)}{(1-q)^{-1}-1}.\)
This means in average \(\frac {n}{l}\) observations in a single year.
Special case of Theorem 2.6 in Coles (2001).
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Acknowledgments
P. Rakonczai’s research was supported by an whitei OTKA mobility grant (OTKA registration number: MB08A 84576, PKR registration number: HUMAN-MB08-1-2011-0007). The work of L. Varga was supported by the European Union Social Fund (Grant Agreement No. TÁMOP 4.2.1/B-09/1/KMR-2010-0003).
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Varga, L., Rakonczai, P. & Zempléni, A. Applications of threshold models and the weighted bootstrap for Hungarian precipitation data. Theor Appl Climatol 124, 641–652 (2016). https://doi.org/10.1007/s00704-015-1438-6
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DOI: https://doi.org/10.1007/s00704-015-1438-6