eye {tea}

Automated Approach for Interpreting the Hill-Plot

Description

An Implementation of the so called Eye-balling Technique proposed in Danielsson et al. (2016)

Usage

eye(data, ws = 0.01, epsilon = 0.3, h = 0.9)

Arguments

data

vector of sample data

ws

size of the moving window. Default is one percent of the data

epsilon

size of the range in which the estimates can vary

h

percentage of data inside the moving window that should lie in the tolerable range

Details

The procedure searches for a stable region in the Hill-Plot by defining a moving window. Inside this window the estimates of the Hill estimator with respect to k have to be in a pre-defined range around the first estimate within this window. It is sufficient to claim that only h percent of the estimates within this window lie in this range. The smallest k that accomplishes this is then the optimal number of upper order statistics, i.e. data in the tail.

Value

k0

optimal number of upper order statistics, i.e. number of exceedances or data in the tail

threshold

the corresponding threshold

tail.index

the corresponding tail index by plugging in k0 into the hill estimator

References

Danielsson, J. and Ergun, L.M. and de Haan, L. and de Vries, C.G. (2016). Tail Index Estimation: Quantile Driven Threshold Selection.

Examples

data(danish)
eye(danish)