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Asymptotic results for sample autocovariance functions and extremes of integrated generalized Ornstein-Uhlenbeck processes
continuous-time GARCH process extreme value theory generalizedOrnstein–Uhlenbeck process integrated generalized Ornstein–Uhlenbeck process
2010/3/10
We consider a positive stationary generalized Ornstein–Uhlenbeck process
Vt = e−tZ t0es− ds + V0 for t 0,and the increments of the integrated generalized Ornstein–Uhlenbeck process...
We prove a large deviations principle (LDP) for partial
sums U-processes indexed by the half line. The LDP can be formulated
on a suitable subset of the set of all absolutely continuous paths. We
e...
Expansions for Quantiles and Multivariate Moments of Extremes for Distributions of Pareto Type
Bell polynomials Extremes Inversion theorem Moments Pareto Quantiles
2010/3/19
Let Xnr be the rth largest of a random sample of size n from a distribution
F(x) = 1 −P∞i=0 cix− −i for > 0 and > 0. An inversion theorem is proved and used to
derive an expan...
Let X(t) t 0 ,X(0) = 0, be a L´evy process with spectral L´evy measure . Assuming that ((−1, 0)) < 1 and the right tail of is light, we show that in the presence of Brownian co...
Statistics of extremes by oracle estimation
Nonparametric adaptive estimation extreme values Hill estimator probabilities of rare events high quantiles
2010/4/30
We use the fitted Pareto law to construct an accompanying approximation
of the excess distribution function. A selection rule of
the location of the excess distribution function is proposed based on...