00fMultivar-package: Modelling Multivariate Return Distributions

In fMultivar: Rmetrics - Modeling of Multivariate Financial Return Distributions

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

Package:	fMultivar
Type:	Package
Version:	R 3.0.1
Date:	2014
License:	GPL Version 2 or later
Copyright:	(c) 1999-2014 Rmetrics Assiciation
URL:	https://www.rmetrics.org

1 Introduction

The package 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 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 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).

2 Bivariate Distributions

This section contains functions to model bivariate density, probability, quantile functions, and to generate random numbers for three standard distributions.

  [dpr]cauchy2d         Bivariate Cauchy Distribution
  [dpr]norm2d           Bivariate Normal Disribution
  [dpr]t2d              Bivariate Student-t Disribution
  

The density function

  delliptical2d         Bivariate Elliptical Densities
  

computes for several bivariate elliptical distributions their densities. Included distributions are the following types: "norm", "cauchy", "t", "logistic", "laplace", "kotz", and "epower".

3 Multivariate Symmetric Distributions

  [dpr]              Multivariate Cauchy Distribution
  [dpr]              Multivariate Normal Distribution
  [dpr]              Multivariate Student-t Distribution
  
  [dpr]              Multivariate Truncated Normal Distribution
  

3 Multivariate Skew Distributions

We use the functions from the contributed package "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:

  [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 fMultivar package they depend on the "sn" package and are loaded when fMultivar is loaded.

NOTE: In the new version of the fMultivar package the following two distribution functions *mvsnorm (multivariate Normal distribution) and *mvst (multivariate Student-t Distribution) will become obsolete together with the mvFit parameter estimation function. The functionality is fully covered by the "sn" package. (They will be most likely deprecated in the future.)

For parameter estimation please use the simple wrapper functions:

  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.

4 Multivariate GHYP Distributions

We refer to the package "ghyp" authored by David Luethi and Wolfgang Breymann,

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:

  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:

  integrate2d           Bivariate Integration
  adapt                 Multivariate adaptive Quadratur
  

The function adapt is a wrapper to the function adaptIntegrate from the new contributed package cubature authored by Stephan G. Johnson.

About Rmetrics:

The fMultivar Rmetrics package is written for educational support in teaching "Computational Finance and Financial Engineering" and licensed under the GPL.

fMultivar documentation built on July 9, 2023, 3:08 p.m.