chf_NTS: chf_NTS

In aaron9011/temStaR-v0.90: Tempered Stable Distribution

chf_NTS

Description

chf_NTS calculates Ch.F of the NTS distribution with parameters (\alpha, \theta, \beta, \gamma, \mu). If a time parameter value is given, it calculates Ch.F of the NTS profess \phi(u)=E[\exp(i u (X(t+s)-X(s)) )]=\exp(t \log(E[\exp(i u X(1))])), where X is the NTS process generated by the NTS distribution with parameters (\alpha, \theta, \beta, \gamma, \mu).

Usage

chf_NTS(u, param)

Arguments

u	An array of u
ntsparam	A vector of the NTS parameters (\alpha, \theta, \beta, \gamma, \mu). For NTS process case it is a vector of parameters (\alpha, \theta, \beta, \gamma, \mu, t).

Value

Characteristic function of the NTS distribution

Examples

library(functional)
library(nloptr)
library(pracma)
library(spatstat)
library(Matrix)
library("temStaR")
alpha <- 1.2
theta <- 1
beta <- -0.2
gamma <- 0.3
mu <- 0.1
ntsparam <- c(alpha, theta, beta, gamma, mu)
u <- seq(from = -2*pi, to = 2*pi, length.out = 101)
phi <- chf_NTS(u, ntsparam)


#Annual based parameters
alpha <- 1.2
theta <- 1
beta <- -0.2
gamma <- 0.3
mu <- 0.1
#scaling annual parameters to one day
dt <- 1/250 #one day
ntsparam <- c(alpha, theta, beta, gamma, mu, dt)
u <- seq(from = -2*pi, to = 2*pi, length.out = 101)
phi <- chf_NTS(u, ntsparam)

aaron9011/temStaR-v0.90 documentation built on June 1, 2025, 4:15 p.m.