Modeling extreme events: Time-varying extreme tail shape

Arbeitspapier

We propose a dynamic semi-parametric framework to study time variation in tail parameters. The framework builds on the Generalized Pareto Distribution (GPD) for modeling peaks over thresholds as in Extreme Value Theory, but casts the model in a conditional framework to allow for time-variation in the tail shape parameters. The score-driven updates used improve the expected Kullback-Leibler divergence between the model and the true data generating process on every step even if the GPD only fits approximately and the model is mis-specified, as will be the case in any finite sample. This is confirmed in simulations. Using the model, we find that Eurosystem sovereign bond purchases during the euro area sovereign debt crisis had a beneficial impact on extreme upper tail quantiles, leaning against the risk of extremely adverse market outcomes while active.

Object Details

• ISBN: 978-92-899-4524-0
• Language: Englisch

References and Relationships

• Bibliographic citation: Series: ECB Working Paper ; No. 2524

Classification and Topics

• Classification: Wirtschaft ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Portfolio Choice; Investment Decisions
• Subject: dynamic tail risk ; observation-driven models ; extreme value theory ; EuropeanCentral Bank (ECB) ; Securities Markets Programme (SMP)

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Schwaab, Bernd ; Zhang, Xin ; Lucas, André
• Event: Veröffentlichung
• (who): European Central Bank (ECB)
• (where): Frankfurt a. M.
• (when): 2021

Further information

• DOI: doi:10.2866/252648
• Handle: http://hdl.handle.net/10419/234078
• Last update: 10.03.2025, 11:45 AM CET