*Tid:* **2 oktober 2017 kl 15.15-16.15.**
**Seminarierummet F11**, Institutionen för
matematik, KTH, Lindstedtsvägen 22.
*Föredragshållare:*
**
Holger Drees
**
**Titel:**
Analysis of the Extremal Dependence Structure of Time Series
with Applications to Financial Modeling
**Abstract**
The extremal dependence structure of a regularly varying stationary time series (Xt)t2Z
is captured by the so-called spectral tail process, whose distribution is dened via the
limit of the conditional distribution of (X_-s/|X_0|,..., X_t/|X_0|) given that |X_0| > u. A
natural estimator of the marginal cdf's of the spectral tail process can be constructed by
replacing these unknown probabilities with empirical counterparts.
However, Basrak and Segers (2009) established the so-called time change formula which
describes the relationship between the distribution of the spectral tail process shifted in
time and the distribution of the original spectral tail process. This formula can be used
to derive alternative estimators for the marginal cdf's which are often more efficient than
the direct estimator.
The limit distributions of these estimators are too complex to directly enable the construction of confidence regions. Time permitting, we will discuss how multiplier block
bootstrap can be used for this purpose.
The methodology will be applied to select between GARCH-type models with distinct
extreme value behavior.
(The talk is based on joint work with Richard Davis, Johan Segers and Michal Warchol)
References
Basrak, B., and Segers, J. (2009). Regularly varying multivariate time series. * Stoch. Proc.
Appl.* 119, 1055-1080.
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