We present several notions of high-level dependence for stochastic processes,
which have appeared in the literature. We calculate such measures for discrete
and continuous-time models, where we concentrate on time series with heavy-tailed
marginals, where extremes are likely to occur in clusters. Such models include linear
models and solutions to random recurrence equations; in particular, discrete and
continuous-time moving average and (G)ARCH processes. To illustrate our results
we present a small simulation study. «
We present several notions of high-level dependence for stochastic processes,
which have appeared in the literature. We calculate such measures for discrete
and continuous-time models, where we concentrate on time series with heavy-tailed
marginals, where extremes are likely to occur in clusters. Such models include linear
models and solutions to random recurrence equations; in particular, discrete and
continuous-time moving average and (G)ARCH processes. To illustrate our results
we pres... »
Stichworte:
ARCH, COGARCH, extreme cluster, extreme dependence measure, extremal index, extreme value theory, GARCH, linear model, multivariate regular variation, nonlinear model, Lévy-driven Ornstein-Uhlenbeck process, random recurrence equation