rd <- c(1, 5, 10, 20, 40) yrets <- na.omit(matrix(unlist(lapply(rd, function(x) diff(log(y), lag = x))), ncol = 5)) ## Function for xi/chi coefficients xichi <- function(x){ param <- coef(x, type = "alpha.delta") rho <- param[["beta"]] / param[["alpha"]] zeta <- param[["delta"]] * sqrt(param[["alpha"]]^2 - param[["beta"]]^2) xi <- 1 / sqrt(1 + zeta) chi <- xi * rho result <- c(chi, xi) names(result) <- c("chi", "xi") return(result) } ## HYP Fitting hypfits <- apply(yrets, 2, fit.hypuv, symmetric = FALSE) points <- matrix(unlist(lapply(hypfits, xichi)), ncol = 2, byrow = TRUE) ## Shape triangle col.def <- c("black", "blue", "red", "green", "orange") leg.def <- paste(rd, rep("day return", 5)) plot(points, ylim = c(-0.2, 1.2), xlim = c(-1.2, 1.2), col = col.def, pch = 16, ylab = expression(xi), xlab = expression(chi)) lines(x = c(0, -1), y = c(0, 1)) lines(x = c(0, 1), y = c(0, 1)) lines(x = c(-1, 1), y = c(1, 1)) legend("bottomright", legend = leg.def, col = col.def, pch = 16) text(x = 0.0, y = 1.05, label = "Laplace", srt = 0) text(x = -1.0, y = 1.05, label = "Exponential", srt = 0) text(x = 1.0, y = 1.05, label = "Exponential", srt = 0) text(x = 0.0, y = -0.1, label = "Normal", srt = 0) text(x = -0.6, y = 0.5, label = "Hyperbolic, left skewed", srt = 302) text(x = 0.6, y = 0.5, label = "Hyperbolic, right skewed", srt = 57)