AssetsModelling {fAssets} | R Documentation |
A collection and description of functions which
generate multivariate artificial data sets of assets,
and fit the parameters to a multivariate normal,
skew normal, or (skew) Student-t distribution and
which compute some benchmark statistics.
The functions are:
assetsSim | Simulates a data set of assets, |
assetsSelect | Asset Selection from Portfolios, |
assetsFit | Fits the parameter of a data set of assets, |
print | S3 print method for an object of class 'fASSETS', |
plot | S3 Plot method for an object of class 'fASSETS", |
summary | S3 summary method for an object of class 'fASSETS'. |
assetsSim(n, dim = 2, model = list(mu = rep(0, dim), Omega = diag(dim), alpha = rep(0, dim), df = Inf), assetNames = NULL) assetsFit(x, method = c("st", "snorm", "norm"), title = NULL, description = NULL, fixed.df = NA, ...) show.fASSETS(object) ## S3 method for class 'fASSETS': plot(x, which = "ask", ...) ## S3 method for class 'fASSETS': summary(object, which = "all", ...)
assetNames |
[assetsSim] - a vector of character strings of length dim allowing
for modifying the names of the individual assets.
|
description |
[assetsFit] - a character string, assigning a brief description to an "fASSETS" object.
|
fixed.df |
[assetsFit] - either NA , the default, or a numeric value assigning the
number of degrees of freedom to the model. In the case that
fixed.df=NA the value of df will be included in the
optimization process, otherwise not.
|
method |
[assetsFit] - a character string, which type of distribution should be fitted? method="st" denotes a multivariate skew-Student-t distribution,
method="snorm" a multivariate skew-Normal distribution, and
method="norm" a multivariate Normel distribution.
By default a multivariate normal distribution will be fitted to the
empirical market data.[assetsMeanVar] - a character string, whicht determines how to compute the covariance matix. If method="cov" is selected then the standard
covariance will be computed by R's base function cov , if
method="shrink" is selected then the covariance will be
computed using the shrinkage approach as suggested in Schaefer and
Strimmer [2005], if method="bagged" is selected then the
covariance will be calculated from the bootstrap aggregated (bagged)
version of the covariance estimator.[assetsSelect] - a character string, which clustering method should be applied? Either hclust for hierarchical clustering of dissimilarities,
or kmeans for k-means clustering.[assetsTest] - a character string, which the selects which test should be applied. If method="shapiro" then Shapiro's multivariate Normality
test will be applied as implemented in R's contributed package
mvnormtest . If method="energy" then the E-statistic
(energy) for testing multivariate Normality will be used as proposed
and implemented by Szekely and Rizzo [2005] using parametric
bootstrap.
|
model |
[assetsSim] - a list of model parameters: mu a vector of mean values, one for each asset series, Omega the covariance matrix of assets, alpha the skewness vector, and df the number of degrees of freedom which is a measure for
the fatness of the tails (excess kurtosis). For a symmetric distribution alpha is a vector of zeros.
For the normal distributions df is not used and set to
infinity, Inf . Note that all assets have the same value
for df .
|
n, dim |
[assetsSim] - integer values giving the number of data records to be simulated, and the dimension of the assets set. |
object |
[show][summary] - An object of class fASSETS .
|
title |
[assetsFit] - a character string, assigning a title to an "fASSETS" object.
|
which |
which of the five plots should be displayed? which can
be either a character string, "all" (displays all plots)
or "ask" (interactively asks which one to display), or a
vector of 5 logical values, for those elements which are set
TRUE the correponding plot will be displayed.
|
x |
[assetsFit] - a numeric matrix of returns or any other rectangular object like a data.frame or a multivariate time series object which can be transformed by the function as.matrix to an object of
class matrix .
|
... |
optional arguments to be passed. |
Assets Objects:
Data sets of assets x
can be expressed as multivariate
'timeSeries' objects, as 'data.frame' objects, or any other rectangular
object which can be transformed into an object of class 'matrix'.
Parameter Estimation:
The function assetsFit
for the parameter estimation and
assetsSim
for the simulation of assets sets use code based on
functions from the contributed packages "mtvnorm"
and "sn"
.
The required functionality for fitting data to a multivariate Normal,
skew-Normal, or skew-Student-t is available from builtin functions, so
it is not necessary to load the packages "mtvnorm"
and "sn"
.
assetsFit()
returns a S4 object class of class "fASSETS"
, with the following
slots:
@call |
the matched function call. |
@data |
the input data in form of a data.frame. |
@description |
allows for a brief project description. |
@fit |
the results as a list returned from the underlying fitting function. |
@method |
the selected method to fit the distribution, one
of "norm" , "snorm" , "st" .
|
@model |
the model parameters describing the fitted parameters in
form of a list, model=list(mu, Omega, alpha, df .
|
@title |
a title string. |
@fit$dp |
a list containing the direct parameters beta, Omega, alpha.
Here, beta is a matrix of regression coefficients with
dim(beta)=c(nrow(X), ncol(y)) , Omega is a
covariance matrix of order dim , alpha is
a vector of shape parameters of length dim .
|
@fit$se |
a list containing the components beta, alpha, info. Here, beta and alpha are the standard errors for the corresponding point estimates; info is the observed information matrix for the working parameter, as explained below. |
fit@optim |
the list returned by the optimizer optim ; see the
documentation of this function for explanation of its
components.
|
Note that the @fit$model
slot can be used as input to the
function assetsSim
for simulating a similar portfolio of
assets compared with the original portfolio data, usually market
assets.
assetsSim()
returns a matrix, the artifical data records represent the assets
of the portfolio. Row names and column names are not created, they
have to be added afterwards.
Adelchi Azzalini for R's sn
package,
Torsten Hothorn for R's mtvnorm
package,
Diethelm Wuertz for the Rmetrics port.
Azzalini A. (1985); A Class of Distributions Which Includes the Normal Ones, Scandinavian Journal of Statistics 12, 171–178.
Azzalini A. (1986); Further Results on a Class of Distributions Which Includes the Normal Ones, Statistica 46, 199–208.
Azzalini A., Dalla Valle A. (1996); The Multivariate Skew-normal Distribution, Biometrika 83, 715–726.
Azzalini A., Capitanio A. (1999); Statistical Applications of the Multivariate Skew-normal Distribution, Journal Roy. Statist. Soc. B61, 579–602.
Azzalini A., Capitanio A. (2003); Distributions Generated by Perturbation of Symmetry with Emphasis on a Multivariate Skew-t Distribution, Journal Roy. Statist. Soc. B65, 367–389.
Genz A., Bretz F. (1999); Numerical Computation of Multivariate t-Probabilities with Application to Power Calculation of Multiple Contrasts, Journal of Statistical Computation and Simulation 63, 361–378.
Genz A. (1992); Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics 1, 141–149.
Genz A. (1993); Comparison of Methods for the Computation of Multivariate Normal Probabilities, Computing Science and Statistics 25, 400–405.
Hothorn T., Bretz F., Genz A. (2001); On Multivariate t and Gauss Probabilities in R, R News 1/2, 27–29.
MultivariateDistribution
.
## berndtInvest - data(berndtInvest) # Select "CONTIL" "DATGEN" "TANDY" and "DEC" Stocks: select = c("CONTIL", "DATGEN", "TANDY", "DEC") # Convert into a timeSeries object: berndtAssets.tS = as.timeSeries(berndtInvest)[, select] head(berndtAssets.tS) # Plot Prices: prices = apply(berndtAssets.tS, 2, cumsum) ts.plot(prices, main = "Berndt Assets", xlab = "Number of Months", ylab = "Price", col = 1:4) Legend = colnames(prices) legend(0, 3, legend = Legend, pch = "----", col = 1:4, cex = 1) ## assetsFit - # Fit a Skew-Student-t Distribution: fit = assetsFit(berndtAssets.tS) print(fit) # Show Model Slot: print(fit@model) ## assetsSim - # Simulate set with same statistical properties: set.seed(1953) berndtAssetsSim = assetsSim(n = 120, dim = 4, model = fit@model) colnames(berndtAssetsSim) = paste(select, "SIM", sep = ".") head(berndtAssetsSim) pricesSim = apply(berndtAssetsSim, 2, cumsum) ts.plot(pricesSim, main = "Berndt Assets Simulated", xlab = "Number of Months", ylab = "Simulated Price", col = 1:4) Legend = colnames(pricesSim) legend(0, 6, legend = Legend, pch = "----", col = 1:4, cex = 1)