Ferro-Segers intervals estimator of the extremal index

Ferro and Segers (2003), Eqs. (4) and (34): a moment ratio of the interexceedance times, which converge to a mixture of within-cluster short gaps and exponential between-cluster long ones. NO tuning parameter – the paper's selling point over the runs estimator. The case split (uncorrected when every gap is at most 2, corrected otherwise) is the authors' rule and is followed rather than one form being picked.

Usage

morie_evt_extremal_intervals(x, threshold)

Arguments

x

stationary series.

threshold

exceedance threshold.

Value

list: theta, n_exceedances, form_used, mean_interexceedance, max_interexceedance, implied_mean_cluster_size, threshold, n, method.

References

Ferro and Segers (2003), JRSS-B 65:545-556.

Examples

set.seed(1)
x <- stats::rnorm(500)
morie_evt_extremal_intervals(x, stats::quantile(x, 0.95))$theta
#> [1] 1