Estimation of Mean and Covariances of Asset Sets

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Description

Estimates the mean and/or covariance matrix of a time series of assets by traditional and robust methods.

Usage

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assetsMeanCov(x, 
    method = c("cov", "mve", "mcd", "MCD", "OGK", "nnve", "shrink", "bagged"), 
    check = TRUE, force = TRUE, baggedR = 100, sigmamu = scaleTau2, 
    alpha = 1/2, ...)
    
getCenterRob(object)
getCovRob(object)

Arguments

x

any rectangular time series object which can be converted by the function as.matrix() into a matrix object, e.g. like an object of class timeSeries, data.frame, or mts.

method

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.

check

a logical flag. Should the covariance matrix be tested to be positive definite? By default TRUE.

force

a logical flag. Should the covariance matrix be forced to be positive definite? By default TRUE.

baggedR

when methode="bagged", an integer value, the number of bootstrap replicates, by default 100.

sigmamu

when methode="OGK", a function that computes univariate robust location and scale estimates. By default it should return a single numeric value containing the robust scale (standard deviation) estimate. When mu.too is true (the default), sigmamu() should return a numeric vector of length 2 containing robust location and scale estimates. See scaleTau2, s_Qn, s_Sn, s_mad or s_IQR for examples to be used as sigmamu argument. For details we refer to the help pages of the R-package robustbase.

object

a list as returned by the function assetsMeanCov.

alpha

when methode="MCD", a numeric parameter controlling the size of the subsets over which the determinant is minimized, i.e., alpha*n observations are used for computing the determinant. Allowed values are between 0.5 and 1 and the default is 0.5. For details we refer to the help pages of the R-package robustbase.

...

optional arguments to be passed to the underlying estimators. For details we refer to the manual pages of the functions cov.rob for arguments "mve" and "mcd" in the R package MASS, to the functions covMcd and covOGK in the R package robustbase.

Value

assetsMeanCov returns a list with for entries named center cov, mu and Sigma. The list may have a character vector attributed with additional control parameters.

getCenterRob extracts the center from an object as returned by the function assetsMeanCov.

getCovRob extracts the covariance from an object as returned by the function assetsMeanCov.

Author(s)

Juliane Schaefer and Korbinian Strimmer for R's corpcov package,
Diethelm Wuertz for the Rmetrics port.

References

Breiman L. (1996); Bagging Predictors, Machine Learning 24, 123–140.

Ledoit O., Wolf. M. (2003); ImprovedEestimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection, Journal of Empirical Finance 10, 503–621.

Schaefer J., Strimmer K. (2005); A Shrinkage Approach to Large-Scale Covariance Estimation and Implications for Functional Genomics, Statist. Appl. Genet. Mol. Biol. 4, 32.

Wuertz, D., Chalabi, Y., Chen W., Ellis A. (2009); Portfolio Optimization with R/Rmetrics, Rmetrics eBook, Rmetrics Association and Finance Online, Zurich.

Examples

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## LPP -
   LPP <- as.timeSeries(data(LPP2005REC))[, 1:6]
   colnames(LPP)
   
## Sample Covariance Estimation:
   assetsMeanCov(LPP)
   
## Shrinked Estimation:
   shrink <- assetsMeanCov(LPP, "shrink")
   shrink
   
## Extract Covariance Matrix:
   getCovRob(shrink)