# K-Means Clustering for Heteroscedastic Extremes This function performs k-means clustering for heteroscedastic extremes. UTF-8 ```r khetmeans(y, centers, iter.max = 10, alpha = 0.5) ``` ## 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. ## Returns 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. ## 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 ```r ## Not run: ## 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') ## End(Not run) ## Not run: ## 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)) ## End(Not run) ``` ## Author(s) Miguel de Carvalho, Rodrigo Rubio.

khetmeans function