# Regularly varying multivariate time series

@article{Basrak2007RegularlyVM, title={Regularly varying multivariate time series}, author={Bojan Basrak and J. Segers}, journal={Stochastic Processes and their Applications}, year={2007}, volume={119}, pages={1055-1080} }

Extreme values of a stationary, multivariate time series may exhibit dependence across coordinates and over time. The aim of this paper is to offer a new and potentially useful tool called tail process to describe and model such extremes. The key property is the following fact: existence of the tail process is equivalent to multivariate regular variation of finite cuts of the original process. Certain remarkable properties of the tail process are exploited to shed new light on known results on… Expand

#### 153 Citations

VARYING MULTIVARIATE TIME SERIES

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A regularly varying time series as introduced in Basrak and Segers [1] is a (multivariate) time series such that all finite-dimensional distributions are multivariate regularly varying. The extremal… Expand

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We consider a strictly stationary sequence of random vectors whose finite-dimensional distributions are jointly regularly varying with some positive index. This class of processes includes among… Expand

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To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees et al., (2015) proposed nonparametric estimators of the spectral tail process. The methodology can be extended… Expand

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1 Inference on the tail process with application to financial time series modelling

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To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho l [Extremes (2015) 18, 369–402] proposed nonparametric estimators of the spectral tail… Expand

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