\HeaderA{MultivariateMoments}{functions to compute multivariate moments of a joint distribution}{MultivariateMoments}
\aliasA{CoKurtosisMatrix}{MultivariateMoments}{CoKurtosisMatrix}
\aliasA{CoSkewnessMatrix}{MultivariateMoments}{CoSkewnessMatrix}
\aliasA{kurtosis.MM}{MultivariateMoments}{kurtosis.MM}
\aliasA{M3.MM}{MultivariateMoments}{M3.MM}
\aliasA{M4.MM}{MultivariateMoments}{M4.MM}
\aliasA{multivariate\_mean}{MultivariateMoments}{multivariate.Rul.mean}
\aliasA{skewness.MM}{MultivariateMoments}{skewness.MM}
\aliasA{StdDev.MM}{MultivariateMoments}{StdDev.MM}
\keyword{ts}{MultivariateMoments}
\keyword{multivariate}{MultivariateMoments}
\keyword{distribution}{MultivariateMoments}
\keyword{models}{MultivariateMoments}
\begin{Description}\relax
When worknig with multivariate series, the joint distribution of the returns is to be prefered over the simple univariate distribution of the resulting return vector of a portfolio.  These functions are used internally by PerformanceAnalytics to calculate centered moments for a multivariate distribution as well as the standardized moments of a portfolio distribution.  They are exposed here for users who wish to use them directly, and we'll get more documentation written when we can.
\end{Description}
\begin{Usage}
\begin{verbatim}
M3.MM(R)
M4.MM(R)
StdDev.MM(w, sigma)
skewness.MM(w, sigma, M3)
kurtosis.MM(w, sigma, M4)
CoSkewnessMatrix(R, ...)
CoKurtosisMatrix(R, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{R}] a vector, matrix, data frame, timeSeries or zoo object of asset returns 
\item[\code{w}] a vector of weights to be applied to each asset in trhe joint distribution 
\item[\code{sigma}] variance or second centered moment of the distribution 
\item[\code{M3}] The third mathematical moment of the joint distribution, provided by  \code{\LinkA{M3.MM}{M3.MM}} 
\item[\code{M4}] The fourth mathematical moment of the joint distribution, provided by  \code{\LinkA{M4.MM}{M4.MM}} 
\item[\code{...}] any other passthru parameters 
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
~~ Additional Details will be added to documentation as soon as we have time to write them. ~~
\end{Details}
\begin{Author}\relax
Kris Boudt, Brian Peterson
\end{Author}
\begin{References}\relax
Boudt, Kris, Brian G. Peterson, and Christophe Croux. 2008. Estimation and Decomposition
of Downside Risk for Portfolios with Non-Normal Returns. Journal of Risk. Winter.

Martellini, Lionel, and Volker Ziemann. 2007. Improved Forecasts of Higher-Order Comoments and Implications for Portfolio Selection. EDHEC Risk and Asset Management Research Centre working paper.

Ranaldo, Angelo, and Laurent Favre Sr. 2005. How to Price Hedge Funds: From Two- to
Four-Moment CAPM. SSRN eLibrary.

Scott, Robert C., and Philip A. Horvath. 1980. On the Direction of Preference for Moments of
Higher Order than the Variance. Journal of Finance 35(4):915-919.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{skewness}{skewness}}, \code{\LinkA{kurtosis}{kurtosis}}, \code{\LinkA{MultivariateRisk}{MultivariateRisk}}, \code{\LinkA{centeredmoment}{centeredmoment}}
\end{SeeAlso}

