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\name{fMultivar-package}
\alias{fMultivar-package}
\alias{fMultivar}
\docType{package}
\title{Modelling Multivariate Return Distributions}
\description{
The Rmetrics "fMultivar"" package is a collection of functions
to manage, to investigate and to analyze bivariate and multivariate
data sets of financial returns.
}
\details{
\tabular{ll}{
Package: \tab fMultivar\cr
Type: \tab Package\cr
Version: \tab R 3.0.1\cr
Date: \tab 2014\cr
License: \tab GPL Version 2 or later\cr
Copyright: \tab (c) 1999-2014 Rmetrics Assiciation\cr
URL: \tab \url{https://www.rmetrics.org}
}
}
\section{1 Introduction}{
The package \code{fMultivar} was written to explore and investigate
bivariate and multivariate financial return series.
The bivariate modeling allows us the comparison of financial returns
from two investments or from one investment and its benchmark. When
it comes to the investigation of multiple investment returns from
funds or portfolios we are concerned with the multivariate case.
In the case of bivariate distribution functions we provide functions
for the 2-dimensional Cauchy, Normal, and Student-t distributions.
A generalisation (for the density only) is made for the family of
2-dimensional elliptical distributions. In this case we provide density
functions for the Normal, Cauchy, Student-t, Logistic, Laplace, Kotz,
e-Power distributions.
In the case of multivariate distribution functions from the skew-normal
(SN) family and some related ones we recommend to
use the density funtions, probability functions and random number
generators provided by Azzalini's contributed package \code{sn}.
The family of his SN-distributions cover the skew Cauchy, the skew
Normal, and the skew Student-t distributions. For parameter fitting
we have added three simple wrapper functions for an easy to use
approach to estimate the distributional parameters for financial
return series.
In the case of multivariate distribution functions from the generalized
hyperbolic (GHYP) family and some related ones we recommend to
use the density funtions, probability functions and random number
generators provided by David Luethi and Wolfgang Breymann's contributed
package \code{ghyp}.
The family of their GHYP-distributions cover beside the General
Hyperbolic distribution (GHYP) also the special cases for the
Hyperbolic distribution (HYP), for the Normal Inverse Gaussian
distribution (NIG), for the Variance Gamma distribution (VG), and
for the skewed Student-t distribution (GHST).
}
\section{2 Bivariate Distributions}{
This section contains functions to model bivariate density,
probability, quantile functions, and to generate random numbers
for three standard distributions.
\preformatted{
[dpr]cauchy2d Bivariate Cauchy Distribution
[dpr]norm2d Bivariate Normal Disribution
[dpr]t2d Bivariate Student-t Disribution
}
The density function
\preformatted{
delliptical2d Bivariate Elliptical Densities
}
computes for several bivariate elliptical distributions their
densities. Included distributions are the following types:
\code{"norm"}, \code{"cauchy"}, \code{"t"}, \code{"logistic"},
\code{"laplace"}, \code{"kotz"}, and \code{"epower"}.
}
\section{3 Multivariate Symmetric Distributions}{
\preformatted{
[dpr] Multivariate Cauchy Distribution
[dpr] Multivariate Normal Distribution
[dpr] Multivariate Student-t Distribution
[dpr] Multivariate Truncated Normal Distribution
}
}
\section{3 Multivariate Skew Distributions}{
We use the functions from the contributed package \code{"sn"} package
to model multivariate density and probability functions, and to
generate random numbers for the skew Cauchy, Normal and Student-t
distributions. Note the symmetric case is also included in these
functions. The functions are:
\preformatted{
[dpr]msc Multivariate Skew Cauchy Distribution
[dpr]msn Multivariate Skew Normal Distribution
[dpr]mst Multivariate Skew Student-t Distribution
}
Note the functions are not part of the \code{fMultivar} package they
depend on the \code{"sn"} package and are loaded when \code{fMultivar}
is loaded.
NOTE: In the new version of the \code{fMultivar} package the following
two distribution functions \code{*mvsnorm} (multivariate Normal
distribution) and \code{*mvst} (multivariate Student-t Distribution)
will become obsolete together with the \code{mvFit} parameter
estimation function. The functionality is fully covered by the
\code{"sn"} package. (They will be most likely deprecated in the
future.)
For parameter estimation please use the simple wrapper functions:
\preformatted{
mscFit Multivariate Skew Cauchy Fit
msnFit Multivariate Skew Normal Fit
mstFit Multivariate Skew Student-t Fit
}
Thes parameter estimation functions will be in the same style
as all the other fitting functions in other Rmetrics packages.
}
\section{4 Multivariate GHYP Distributions}{
We refer to the package \code{"ghyp"} authored by
David Luethi and Wolfgang Breymann,
}
\section{5 Utility Functions}{
We have also added some very useful utility functions for the
bivariate case, these include 2-D grid generation, squared and
hexagonal binned histograms, 2-D kernel density estimates,
bivariate histogram plots:
\preformatted{
grid2d Bivariate Square Grid of Coordinates
binning2d Bivariate Square/Hexagonal Binning Plot
density2d Bivariate Kernel Density Plot
hist2d Bivariate Histogram Plot
gridData Bivariate gridded data set
}
For integration we have added two quadratur routines a simple one
for the bivariate case and an adaptive one for the multivariate case:
\preformatted{
integrate2d Bivariate Integration
adapt Multivariate adaptive Quadratur
}
The function \code{adapt} is a wrapper to the function
\code{adaptIntegrate} from the new contributed package
\code{cubature} authored by Stephan G. Johnson.
}
\section{About Rmetrics:}{
The \code{fMultivar} Rmetrics package is written for educational
support in teaching "Computational Finance and Financial Engineering"
and licensed under the GPL.
}
\keyword{package}
|
