Sliding-blocks estimator of the extremal index

Northrop (2015): for a series with extremal index theta, -b log F_hat(block max) is approximately Exp(theta), so theta = 1/mean. SLIDING blocks use each observation in b windows instead of one, and Northrop shows the sliding version has strictly smaller asymptotic variance than the disjoint one – the entire point of preferring it, and both are returned so the comparison is visible. threshold is accepted only for signature parity with the other extremal-index estimators and is ignored.

Usage

morie_evt_extremal_sliding(x, threshold = NULL, block_length = NULL)

Arguments

x

stationary series.

threshold

ignored; present for signature parity.

block_length

block size b; floor(sqrt(n)) when NULL.

Value

list: theta, theta_disjoint, block_length, n_sliding_blocks, n_disjoint_blocks, n, method.

References

Northrop (2015), Extremes 18:585-603.

Examples

set.seed(1)
morie_evt_extremal_sliding(stats::rnorm(400), block_length = 20)$theta
#> [1] 1