Statistics for tail processes of Markov chains
Michal Warchov – PhD student at Université catholique de Louvain, Belgium

If serial dependence at high levels is sufficiently strong, extreme values of a stationary time series may arrive in clusters rather than in isolation. It is a convenient choice to model extremal dependence by the tail process, which captures finite-dimensional limit distributions of the series conditionally on having a shock at a particular time instant. We propose nonparametric estimators for the tail process focusing on univariate and jointly regularly Markov chains. The estimators are applied to stock market data revealing interesting patterns regarding the succession of large losses and gains.


Michal Warchov

I am a PhD student at the Institute of Statistics, Biostatistics and Actuarial Sciences at the Université Catholique de Louvain in Belgium. Before starting my PhD, I obtained a master’s degree in mathematics at the Jagiellonian University and a bachelor degree in finance at the Cracow University of Economics, Poland. I spent the last year of my undergraduate studies in the Statistics Department of Ecole Polytechnique Fédérale de Lausanne in Switzerland and ever since I have been interested in Extreme Value Theory.

 

“Extremes of stationary time series can exhibit cross–sectional and temporal dependence. Such phenomena can be fully characterized by the tail process.”

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