chf_stdNTS: chf_stdNTS

In aaron9011/temStaR-v0.814: Tempered Stable Distribution

Description

chf_stdNTS calculates Ch.F of the standard NTS distribution with parameters (α, θ, β). If a time parameter value is given, it calculates Ch.F of the standard NTS profess φ(u)=E[\exp(i u (X(t+s)-X(s))]=\exp(t \log(E[\exp(i u X(1))])), where X is the standard NTS process generated by the standard NTS distribution with parameters (α, θ, β).

Usage

chf_stdNTS(u, param)

Arguments

u	An array of u
ntsparam	A vector of the standard NTS parameters (α, θ, β). For the standard NTS process case it is a vector of parameters (α, θ, β, t).

Value

Characteristic function of the standatd NTS distribution

Examples

library("temStaR")
alpha <- 1.2
theta <- 1
beta <- -0.2
ntsparam <- c(alpha, theta, beta)
u <- seq(from = -2*pi, to = 2*pi, length.out = 101)
phi <- chf_stdNTS(u, ntsparam)


#Annual based parameters
alpha <- 1.2
theta <- 1
beta <- -0.2
#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_stdNTS(u, ntsparam)

aaron9011/temStaR-v0.814 documentation built on Dec. 24, 2021, 6:16 p.m.