NH: Normal Inverse Gaussian and Hyperbolic Distribution

In QRM: Provides R-Language Code to Examine Quantitative Risk Management Concepts

Description

Functions for fitting uni- and multivariate NIG and HYP distribution.

Usage

fit.NH(data, case = c("NIG", "HYP"), symmetric = FALSE,
       se = FALSE, ...)
fit.mNH(data, symmetric = FALSE, case = c("NIG", "HYP"),
        kvalue = NA, nit = 2000, tol = 1e-10, ...)
MCECMupdate(data, mix.pars, mu, Sigma, gamma, optpars, optfunc,
xieval=FALSE, ...)
MCECM.Qfunc(lambda, chi, psi, delta, eta, xi)
EMupdate(data, mix.pars, mu, Sigma, gamma, symmetric, 
         scaling = TRUE, kvalue = 1)

Arguments

case	character, whether NIG or HYP shall be used.
chi	numeric, chi parameter.
data	numeric, data.
delta	numeric, delta parameter.
eta	numeric, eta parameter.
kvalue	numeric, value to which the determinant of the dispersion matrix is constrained.
lambda	numeric, lambda parameter.
mix.pars	vector, values of lambda, chi and psi.
mu	numeric, value of location parameters.
nit	integer, maximum number of iterations.
optpars	vector, parameters to optimize over.
optfunc	function, the function to be optimized.
psi	numeric, pi parameter.
scaling	logical, whether determinant scaling of Sigma shall be fixed.
se	logical, whether standard errors should be calculated.
Sigma	matrix, value of Sigma.
symmetric	logical, whether symmetric case should be fitted.
tol	numeric, tolerance for convergence.
gamma	numeric, value of gamma
xi	numeric, xi parameter.
xieval	logical, whether log moment xi shall be evaluated.
...	ellipsis, arguments are passed down to optim().

Details

fit.NH(): See pages 78–80 of QRM. Case ‘NIG’ sets lambda = -1/2; case ‘HYP’ sets lambda = 1.
fit.mNH(): Fitting is accomplished by using a variant of the EM algorithm (see pages 81–83 in QRM).
MCECMupdate(): updates estimates of mixing parameters in EM estimation of generalized hyperbolic (see Algorithm 3.14, steps (5) and (6) on page 83 in QRM).
MCECM.Qfunc(): a functional form that must be optimized when fitting members of generalized hyperbolic family with an MCECM algorithm (see function Q2 on page 82 of QRM).
EMupdate(): updates estimates of location (mu), dispersion (Sigma) and skewness (gamma) parameters in EM estimation of multivariate generalized hyperbolic distributions (see pages 81–83 in QRM; in that case k is the determinant of the sample covariance matrix. “EM” is an acronym for for “Expectation-Maximization” type of algorithm used to fit proposed multivariate hyperbolic models to actual data).

Examples

library(QRM)
data(DJ)
r <- returns(DJ) 
s <- window(r[, "MSFT"], "1993-01-01", "2000-12-31")
mod.NIG <- fit.NH(100 * s, method = "BFGS")
## multivariate
stocks <- c("AXP","EK","BA","C","KO","MSFT",
            "HWP","INTC","JPM","DIS")
ss <- window(r[, stocks], "1993-01-01", "2000-12-31")
fridays <- time(ss)[isWeekday(time(ss), wday = 5)]
ssw <- aggregate(ss, by = fridays, FUN = sum)
mod.mNIG <- fit.mNH(ssw, symmetric = FALSE, case = "NIG") 

QRM documentation built on April 14, 2020, 6:49 p.m.