CenteredMoments: calculate centered moments of a joint distribution

Description

the $n$-th centered moment is calculated as equation ^{(n)}(R) = E(R-E(R))^nequation

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.

centeredcomoment (Ra, Rb, p1, p2, normalize = FALSE) centeredmoment (R, power) Return.centered (R, ...) Ipower (power, h)R{ a vector, matrix, data frame, timeSeries or zoo object of asset returns } Ra{ a vector, matrix, data frame, timeSeries or zoo object of asset returns } Rb{ a vector, matrix, data frame, timeSeries or zoo object of index, benchmark, portfolio, or secondary asset returns to compare against } power{ power or moment to calculate } p1{ first power of the comoment } p2{ second power of the comoment } h{ ~~Describe h here~~ } normalize{ whether to standardize the calculation to agree with common usage, or leave the default mathematical meaning } ...{ any other passthru parameters }

These functions were first utilized in Boudt, Peterson, and Croux (2008), and have been subsequently used in our other research.

~~ Additional Details will be added to documentation as soon as we have time to write them. ~~

Ipower Computes the constant $$\int_{-\infty}^{h} z^q \phi'(z)dz$$ needed for the estimation of mES and Component mES where where $\phi'(z)$ is the derivative of the standard gaussian density function and $h$ is typicall modified VaR if you are computing mES or Gaussian VaR if you are computing Gaussian Expected Shortfall.

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.

[object Object] ~~further notes~~

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~~objects to See Also as help, ~~~ ts multivariate distribution models

Description

Arguments