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)