MleRecursionForStudentT: Compute recursively the ML estimators of location and scatter...

In R-Finance/Meucci: Collection of functionality ported from the MATLAB code of Attilio Meucci.

Description

Compute recursively the ML estimators of location and scatter of a multivariate Student t distribution with given degrees of freedom, as described in A. Meucci, "Risk and Asset Allocation", Springer, 2005, section 4.3 - "Maximum likelihood estimators"

Returns

\widehat{μ} = ∑\limits_{t= 1}^{T} \frac{w_{t}}{∑\limits_{s= 1}^{T}w_{s}} x_{t} ,

\widehat{Σ} = \frac{1}{T}∑\limits_{t= 1}^{T}w_{t}(x_{t}-\widehat{μ})(x_{t}-\widehat{μ})^\prime

where, adapted to the Sudent T distribution,

w_{t}\equiv \frac{ν+N}{ν+(x_{t}-\widehat{μ})^\prime \widehat{Σ}^{-1}( x-\widehat{μ}) }

Usage

  MleRecursionForStudentT(x, Nu, Tolerance = 10^(-10))

Arguments

x	: [matrix] (T x N) observations
Nu	: [scalar] degrees of freedom parameter
Tolerance	: [scalar] tolerance parameter. Default: 10^(-10)

Value

Mu : [vector] (N x 1) mean

Sigma : [matrix] (N x N) covariance

Author(s)

Xavier Valls [e-mail]

References

A. Meucci - "Exercises in Advanced Risk and Portfolio Management" http://symmys.com/node/170, "E 188 - Maximum likelihood estimation of a multivariate Student t distribution".

See Meucci's script for "MleRecursionForStudentT.m"

R-Finance/Meucci documentation built on May 8, 2019, 3:52 a.m.