Statistical inference for heavy tailed series with extremal independence

We consider stationary time series $\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each$h \geq 1$, conditionally on$X_0$to exceed a threshold tending to infinity, the conditional distribution of$X_h$suitably normalized converges weakly to a non degenerate distribution. We consider in this paper the estimation of the normalization and of the limiting distribution.$