Rights statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s10687-016-0258-0
Accepted author manuscript, 408 KB, PDF document
Available under license: CC BY-NC
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Bayesian uncertainty management in temporal dependence of extremes
AU - Lugrin, T.
AU - Davison, A. C.
AU - Tawn, J. A.
N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s10687-016-0258-0
PY - 2016/9
Y1 - 2016/9
N2 - Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assumption of long-range independence often seems reasonable, but short-range dependence, i.e., the clustering of extremes, needs attention. The extremal index 0 < ≤ 1 is a natural limiting measure of clustering, but for wide classes of dependent processes, including all stationary Gaussian processes, it cannot distinguish dependent processes from independent processes with = 1. Eastoe and Tawn (Biometrika 99, 43–55 2012) exploit methods from multivariate extremes to treat the subasymptotic extremal dependence structure of stationary time series, covering both 0 < <1 and = 1, through the introduction of a threshold-based extremal index. Inference for their dependence models uses an inefficient stepwise procedure that has various weaknesses and has no reliable assessment of uncertainty. We overcome these issues using a Bayesian semiparametric approach. Simulations and the analysis of a UK daily river flow time series show that the new approach provides improved efficiency for estimating properties of functionals of clusters.
AB - Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assumption of long-range independence often seems reasonable, but short-range dependence, i.e., the clustering of extremes, needs attention. The extremal index 0 < ≤ 1 is a natural limiting measure of clustering, but for wide classes of dependent processes, including all stationary Gaussian processes, it cannot distinguish dependent processes from independent processes with = 1. Eastoe and Tawn (Biometrika 99, 43–55 2012) exploit methods from multivariate extremes to treat the subasymptotic extremal dependence structure of stationary time series, covering both 0 < <1 and = 1, through the introduction of a threshold-based extremal index. Inference for their dependence models uses an inefficient stepwise procedure that has various weaknesses and has no reliable assessment of uncertainty. We overcome these issues using a Bayesian semiparametric approach. Simulations and the analysis of a UK daily river flow time series show that the new approach provides improved efficiency for estimating properties of functionals of clusters.
KW - Asymptotic independence
KW - Bayesian semiparametrics
KW - Conditional extremes
KW - Dirichlet process
KW - Extreme value theory
KW - Extremogram
KW - Risk analysis
KW - Threshold-based extremal index
U2 - 10.1007/s10687-016-0258-0
DO - 10.1007/s10687-016-0258-0
M3 - Journal article
VL - 19
SP - 491
EP - 515
JO - Extremes
JF - Extremes
SN - 1572-915X
IS - 3
ER -