thetaARBB {boodd}R Documentation

Compute the Extremal Index for Non-Atomic Markov Chains Using Pseudo-Regenerative Blocks

Description

This function divides the input dataset into pseudo-blocks for a non-atomic Markov chain using a Nummelin splitting trick with estimated parameters. We use the optimal small set computed by findBestEpsilon function and calculates the extremal index using quantile-based thresholds.

Usage

thetaARBB(X)

Arguments

X

A numeric vector representing the Markov chain.

Details

The function uses GetPseudoBlocks to divide X into blocks using to the estimated Nummelin splitting trick. High quantiles from X are generated and used as thresholds to compute statistics on each block, including sub-maximums and block indices. These statistics are then used to calculate the extremal index, a measure of extreme value clustering, across the blocks.

Value

A numeric vector representing the extremal index at various quantile thresholds.

References

Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.

Bertail, P. and Clémençon, S. (2006). Regeneration-based statistics for Harris recurrent Markov chains. Lecture notes in Statistics, vol. 187, pp. 1-54, Springer.

See Also

GetPseudoBlocks, fastNadaraya, regenboot, smallEnsemble,findBestEpsilon.

Examples


coeff=0.75
X = arima.sim(n=200, list(ar = c(coeff)))
thetaB <- thetaARBB(X)
plot(thetaB)


[Package boodd version 0.1 Index]