Bootstrapping Hill estimator and tail array sums for regularly varying time series

Bernoulli ◽  
2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Carsten Jentsch ◽  
Rafał Kulik
Keyword(s):  
Time Series ◽  
Hill Estimator ◽  
Regularly Varying

scholarly journals One- versus multi-component regular variation and extremes of Markov trees

2020 ◽  
Vol 52 (3) ◽  
pp. 855-878
Author(s):  
Johan Segers
Keyword(s):  
Time Series ◽  
Random Vector ◽  
Regular Variation ◽  
Conditional Independence ◽  
Conditional Distribution ◽  
The Self ◽  
Stationary Time Series ◽  
Markov Tree ◽  
Regularly Varying ◽  
Coupled Random Walks

AbstractA Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of the Markov kernels associated to these pairs, the conditional distribution of the self-normalized random vector when the variable at the root of the tree tends to infinity converges weakly to a random vector of coupled random walks called a tail tree. If, in addition, the conditioning variable has a regularly varying tail, the Markov tree satisfies a form of one-component regular variation. Changing the location of the root, that is, changing the conditioning variable, yields a different tail tree. When the tails of the marginal distributions of the conditioning variables are balanced, these tail trees are connected by a formula that generalizes the time change formula for regularly varying stationary time series. The formula is most easily understood when the various one-component regular variation statements are tied up into a single multi-component statement. The theory of multi-component regular variation is worked out for general random vectors, not necessarily Markov trees, with an eye towards other models, graphical or otherwise.

scholarly journals Tail Dependence for Regularly Varying Time Series

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Ai-Ju Shi ◽  
Jin-Guan Lin
Keyword(s):  
Time Series ◽  
Conditional Probability ◽  
Tail Dependence ◽  
Intensity Measure ◽  
Dependence Function ◽  
Regularly Varying

We use tail dependence functions to study tail dependence for regularly varying (RV) time series. First, tail dependence functions about RV time series are deduced through the intensity measure. Then, the relation between the tail dependence function and the intensity measure is established: they are biuniquely determined. Finally, we obtain the expressions of the tail dependence parameters based on the expectation of the RV components of the time series. These expressions are coincided with those obtained by the conditional probability. Some simulation examples are demonstrated to verify the results we established in this paper.

scholarly journals Regularly varying multivariate time series

2009 ◽  
Vol 119 (4) ◽  
pp. 1055-1080 ◽  
Author(s):  
Bojan Basrak ◽  
Johan Segers
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Regularly Varying

scholarly journals Tail measure and spectral tail process of regularly varying time series

2018 ◽  
Vol 28 (6) ◽  
pp. 3884-3921 ◽  
Author(s):  
Clément Dombry ◽  
Enkelejd Hashorva ◽  
Philippe Soulier
Keyword(s):  
Time Series ◽  
Regularly Varying ◽  
Tail Measure ◽  
Spectral Tail Process
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