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      Peak-over-Threshold Estimators for Spectral Tail Processes: Random vs Deterministic Thresholds

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          Abstract

          The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees et al. (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 estimators have the same limit distributions. This finding is corroborated in a simulation study, but the version using order statistics performs a bit better for finite samples.

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          Most cited references 7

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          Regular variation of GARCH processes

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            Regularly varying multivariate time series

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

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                Author and article information

                Journal
                16 January 2019
                Article
                1901.05501

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                62G32, 62M10, 62G05
                math.ST stat.ME stat.TH

                Methodology, Statistics theory

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