Runs estimator of the extremal index

Smith and Weissman (1994): clusters over exceedances, a new cluster starting when an exceedance is separated from the previous by more than run_length non-exceedances. theta is the reciprocal mean cluster size – the effective number of independent extremes is theta * n, and ignoring it overstates every return level. The run length is a genuine tuning parameter (too short splits clusters, too long merges them); the intervals estimator (morie_evt_extremal_intervals()) has none and is the usual cross-check.

Usage

morie_evt_extremal_runs(x, threshold, run_length = 1L)

Arguments

x

stationary series.

threshold

exceedance threshold.

run_length

separation starting a new cluster.

Value

list: theta, n_exceedances, n_clusters, mean_cluster_size, run_length, threshold, n, method.

References

Smith and Weissman (1994), JRSS-B 56:515-528.

Examples

set.seed(1)
x <- stats::rnorm(500)
morie_evt_extremal_runs(x, stats::quantile(x, 0.95))$theta
#> [1] 0.96