QRM: NH – R documentation

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QRM

NH

Normal Inverse Gaussian and Hyperbolic Distribution

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

Provides R-Language Code to Examine Quantitative Risk Management Concepts

v0.4-31

GPL (>= 2)

Authors

Bernhard Pfaff [aut, cre], Marius Hofert [ctb], Alexander McNeil [aut] (S-Plus original (QRMlib)), Scott Ulmann [trl] (First R port as package QRMlib)

Initial release

2020-02-15

NH

Description

Usage

Arguments

Details

Examples

QRM

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