# Peak-over-threshold estimators for spectral tail processes: random vs deterministic thresholds

@article{Drees2020PeakoverthresholdEF, title={Peak-over-threshold estimators for spectral tail processes: random vs deterministic thresholds}, author={Holger Drees and M. Kne{\vz}evi{\'c}}, journal={Extremes}, year={2020}, pages={1-27} }

The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees et al. (Extremes 18 (3), 369–402, 2015 ) proposed estimators of the marginal distributions of this process based on exceedances over high deterministic thresholds and analyzed their asymptotic behavior. In practice, however, versions of the estimators are applied which use exceedances over random thresholds like intermediate order statistics. We prove that these modified…

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## References

SHOWING 1-10 OF 18 REFERENCES

### Statistics for tail processes of Markov chains

- Mathematics
- 2014

At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the…

### Inference on the tail process with application to financial time series modeling

- Mathematics, EconomicsJournal of Econometrics
- 2018

### The tail empirical process of regularly varying functions of geometrically ergodic Markov chains

- MathematicsStochastic Processes and their Applications
- 2019

### Extreme quantile estimation for dependent data with applications to finance

- Mathematics
- 2003

The asymptotic normality of a class of estimators for extreme quantiles is established under mild structural conditions on the observed stationary \beta-mixing time series. Consistent estimators of…

### Bootstrapping Empirical Processes of Cluster Functionals with Application to Extremograms

- Mathematics
- 2015

In the extreme value analysis of time series, not only the tail behavior is of interest, but also the serial dependence plays a crucial role. Drees and Rootz\'en (2010) established limit theorems for…

### The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains

- Mathematics
- 2013

We introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums…

### Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)-Processes

- Mathematics
- 2009

This paper collects some of the well known probabilistic properties of GARCH(p, q) processes. In particular, we address the question of strictly and of weakly stationary solutions. We further…

### Towards estimating extremal serial dependence via the bootstrapped extremogram

- Mathematics, Economics
- 2012