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**
We consider the estimation of the conditional expectation E(Xh|X0 > QX(1 −
p)) at extreme levels, where (Xt)t∈Z is a strictly stationary β−mixing time
series, QX its associated quantile function, p ∈ (0, 1) and h a positive integer.
We use the multivariate regular variation framework and start to consider the
case of non-negative time series. A two-step method is used in order to propose
an estimator of this risk measure: first, by introducing an estimator in the
intermediate case and, then, by extrapolating outside the data by a Weissmantype
construction. Under suitable assumptions, we prove the weak convergence
of the estimator of this risk measure. Subsequently, we extend our approach
to the case of real-valued time series by using the decomposition of the original
time series into the positive and negative parts and we prove again the weak
convergence of the proposed estimator under additional assumptions. Some
simulations are provided in order to illustrate the performance of our estimator.
**

V. Chavez et F. Baeriswyl

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