CenteredMoments {PerformanceAnalytics} | R Documentation |
the $n$-th centered moment is calculated as begin{equation} μ^{(n)}(R) = Elbrack(R-E(R))^nrbrack end{equation}
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.
....
~~further notes~~
~Make other sections like Warning with section{Warning }{....} ~
~~who you are~~
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.
~~objects to See Also as help
, ~~~