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

Description Usage Arguments Value References Examples

fitnts fit parameters (α, θ, β, γ, μ) of the NTS distribution. This function using the curvefit method between the empirical cdf and the NTS cdf.

fitnts(rawdat)
fitnts(rawdat), ksdensityflag = 1
fitnts(rawdat, initialparam = c(alpha, theta, beta, gamma, mu))
fitnts(rawdat, initialparam = c(alpha, theta, beta, gamma, mu)), ksdensityflag = 1
fitnts(rawdat, initialparam = c(alpha, theta, beta, gamma, mu)), maxeval = 100, ksdensityflag = 1

`rawdat`	Raw data to fit the parameters.
`initialparam`	A vector of initial NTS parameters. This function uses the `nloptr` package. If it has a good initial parameter then estimation performs better. If users do not know a good initial parameters, then just set it as `initialparam=NaN`, that is default. The function `cffitnts()` may be helpful to find the initial parameters.
`maxeval`	Maximum evaluation number for `nloptr`. The iteration stops on this many function evaluations.
`ksdensityflag`	This function fit the parameters using the curvefit method between the empirical cdf and the NTS cdf. If `ksdensityflag = 1` (default), then the empirical cdf is calculated by the kernel density estimation. If `ksdensityflag = 0`, then the empirical cdf is calculated by the empirical cdf.

Estimated parameters

Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk https://arxiv.org/pdf/2007.13972.pdf

library("temStaR")
library("quantmod")
getSymbols("^GSPC", src="yahoo", from = "2010-1-1", to = "2020-12-31")
pr <- as.numeric(GSPC$GSPC.Adjusted)
ret <- diff(log(pr))
ntsparam <-  fitnts(ret)

Femp = ecdf(ret)
x = seq(from=min(ret), to = max(ret), length.out = 100)
cemp = Femp(x)
ncdf = pnts(x, c(ntsparam))
plot(x,ncdf,type = 'l', col = "red")
points(x,cemp, type = 'l', col = "blue")
a = density(ret)
p = dnts(x,ntsparam)
plot(x,p,type = 'l', col = "red")
lines(a,type = 'l', col = "blue")