Raw2Cumul: Transforms raw moments into cumulants
In R-Finance/Meucci: Collection of functionality ported from the MATLAB code of Attilio Meucci.
Description
Usage
Arguments
Details
Value
Author(s)
References
Description
Step 3 of the projection process: From the non-central
moments of X-t, we compute the cumulants.
Usage
1
Raw2Cumul(mu_)
Arguments
mu_
: [vector] (length N corresponding to order N)
corresponding raw moments
Details
This process follows from the Taylor approximations for
any small z and ln(1+x)~x for any small x, and from the
definition of the first cumulant in (17). The we apply
recursively the identity in formula (21). See Kendall and
Stuart (1969)
κ^{ \big(n\big) }_{X} \equiv \tilde{ μ } ^{
\big(n\big) }_{X} - ∑_{k=1}^{n-1} (n-1)C_{k-1}
κ_{X}^{ \big(k\big) } \tilde{ μ } ^{n-k}_{X}
Value
ka : [vector] (length N corresponding to order N)
cumulative moments
Author(s)
Ram Ahluwalia rahluwalia@gmail.com
References
A. Meucci - "Annualization and General Projection of
Skewness, Kurtosis and All Summary Statistics" - formula
(21) Symmys site containing original MATLAB source code
http://www.symmys.com/node/136
A. Meucci - "Exercises in Advanced Risk and Portfolio
Management" http://symmys.com/node/170. See
Meucci's script for "Raw2Cumul.m"
R-Finance/Meucci documentation built on May 8, 2019, 3:52 a.m.
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Description Usage Arguments Details Value Author(s) References
Description
Step 3 of the projection process: From the non-central moments of X-t, we compute the cumulants.
Usage
1 | Raw2Cumul(mu_)
|
Arguments
mu_ |
: [vector] (length N corresponding to order N) corresponding raw moments |
Details
This process follows from the Taylor approximations for any small z and ln(1+x)~x for any small x, and from the definition of the first cumulant in (17). The we apply recursively the identity in formula (21). See Kendall and Stuart (1969)
κ^{ \big(n\big) }_{X} \equiv \tilde{ μ } ^{ \big(n\big) }_{X} - ∑_{k=1}^{n-1} (n-1)C_{k-1} κ_{X}^{ \big(k\big) } \tilde{ μ } ^{n-k}_{X}
Value
ka : [vector] (length N corresponding to order N) cumulative moments
Author(s)
Ram Ahluwalia rahluwalia@gmail.com
References
A. Meucci - "Annualization and General Projection of Skewness, Kurtosis and All Summary Statistics" - formula (21) Symmys site containing original MATLAB source code http://www.symmys.com/node/136
A. Meucci - "Exercises in Advanced Risk and Portfolio Management" http://symmys.com/node/170. See Meucci's script for "Raw2Cumul.m"
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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