extremis (version 1.2.1)

khetmeans: K-Means Clustering for Heteroscedastic Extremes

Description

This function performs k-means clustering for heteroscedastic extremes.

Usage

khetmeans(y, centers, iter.max = 10, alpha = 0.5)

Value

khetmeans returns an object of class "khetmeans" which has a fitted method. It is a list with at least the following components:

mus.new

cluster center scedasis density.

mugamma.new

cluster center extreme value index.

clusters

cluster allocation.

Y

raw data.

n.clust

number of clusters.

The plot method depicts the k-means clustering for heteroscedastic extremes. If c.c is TRUE, the method displays the cluster means.

Arguments

y

data frame from which the estimate is to be computed; first column corresponds to time and the second to the remainder of interest.

centers

the number of clusters or a set of initial (distinct) cluster centres. If a number, a random set of (distinct) rows in y is chosen as the initial centers.

iter.max

the maximum number of iterations allowed. The default is 10.

alpha

the tuning parameter. The default is 0.5.

Author

Miguel de Carvalho, Rodrigo Rubio.

Details

The intermediate sequence \(\kappa_T\) is chosen proportional to \(T/\log T\).

References

Rubio, R., de Carvalho, M. and Huser, R. (2018) Similarity-Based Clustering of Extreme Losses from the London Stock Exchange. Submitted.

Examples

if (FALSE) {
## Example 1  (Scenario B, T = 5000)
## This example requires package evd 
require(evd)
set.seed(12)
T <- 5000
n <- 30
b <- 0.1
gamma1 <- 0.7
gamma2 <- 1
grid <- seq(0, 1, length = 100)
c2 <- function(s)
    dbeta(s, 2, 5)
c3 <- function(s)
    dbeta(s, 5, 2)
X <- matrix(0, ncol = T, nrow = n)
for(i in 1:5)
  for(j in 1:T)
    X[i,  j] <- rgev(1, c2(j / T), c2(j / T), gamma1)
for(i in 6:15)
  for(j in 1:T)
    X[i,  j] <- rgev(1, c2(j / T), c2(j / T), gamma2)
for(i in 16:20)
  for(j in 1:T)
    X[i,  j] <- rgev(1, c3(j / T), c3(j / T), gamma1)
for(i in 21:30)
  for(j in 1:T)
    X[i,  j] <- rgev(1, c3(j / T), c3(j / T), gamma2)
Y <- t(X)
fit <- khetmeans(Y, centers = 4)
plot(fit, c.c = TRUE)
lines(grid, c2(grid), type = 'l', lwd = 8, col = 'black')
lines(grid, c3(grid), type = 'l', lwd = 8, col = 'black')
}

if (FALSE) {
## Example 2 (Overlapping version of Fig. 5 in Supplementary Materials)
data(lse)
attach(lse)
y <- -apply(log(lse[, -1]), 2, diff)
fit <- khetmeans(y, centers = 3)
plot(fit, c.c = TRUE, ylim = c(0, 3))
}