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2018 Inference for heavy tailed stationary time series based on sliding blocks
Axel Bücher, Johan Segers
Electron. J. Statist. 12(1): 1098-1125 (2018). DOI: 10.1214/18-EJS1415


The block maxima method in extreme value theory consists of fitting an extreme value distribution to a sample of block maxima extracted from a time series. Traditionally, the maxima are taken over disjoint blocks of observations. Alternatively, the blocks can be chosen to slide through the observation period, yielding a larger number of overlapping blocks. Inference based on sliding blocks is found to be more efficient than inference based on disjoint blocks. The asymptotic variance of the maximum likelihood estimator of the Fréchet shape parameter is reduced by more than 18%. Interestingly, the amount of the efficiency gain is the same whatever the serial dependence of the underlying time series: as for disjoint blocks, the asymptotic distribution depends on the serial dependence only through the sequence of scaling constants. The findings are illustrated by simulation experiments and are applied to the estimation of high return levels of the daily log-returns of the Standard & Poor’s 500 stock market index.


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Axel Bücher. Johan Segers. "Inference for heavy tailed stationary time series based on sliding blocks." Electron. J. Statist. 12 (1) 1098 - 1125, 2018.


Received: 1 June 2017; Published: 2018
First available in Project Euclid: 27 March 2018

zbMATH: 06864486
MathSciNet: MR3780041
Digital Object Identifier: 10.1214/18-EJS1415

Primary: 62G32
Secondary: 62M10

Keywords: Apéry’s constant , Block maxima , Fréchet distribution , Marshall–Olkin distribution , maximum likelihood estimator , Pickands dependence function , return level


Vol.12 • No. 1 • 2018
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