ComputeMVE: Compute the minimum volume ellipsoid for a given...

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

Description

Function computes the minimum volume ellipsoid for a given time series

Usage

  ComputeMVE(data)

Arguments

data	a matrix time-series of data. Each row is a observation (date). Each column is an asset

Details

via the expectations-minimization algorithm

w_{t} = \frac{1}{T} , t = 1,...,T \\ m \equiv \frac{1}{ ∑_{s=1}^T w_{s} } ∑_{t=1}^T w_{t} x_{t} \\ S \equiv ∑_{t=1}^T w_{t} \big(x_{t} - m\big) \big(x_{t} - m\big)' \\ Ma_{t}^{2} \equiv \big(x-m\big)' S^{-1} \big(x-m\big), t=1,...,T \\ w_{t} \mapsto w_{t} Ma_{t}^{2} \\ U = \big(x_{1}' - \hat{E}',...,x_{T}' - \hat{E}' \big) \\ \hat{Cov} \equiv \frac{1}{T} U'U

The location and scatter parameters that define the ellipsoid are multivariate high-breakdown estimators of location and scatter

Value

list a list with MVE_Location a numeric with the location parameter of minimum volume ellipsoid MVE_Dispersion a numeric with the covariance matrix of the minimum volume ellipsoid

Author(s)

Ram Ahluwalia [e-mail]

References

http://www.symmys.com/sites/default/files/Risk%20and%20Asset%20Allocation%20-%20Springer%20Quantitative%20Finance%20-%20Estimation.pdf See Sec. 4.6.1 of "Risk and Asset Allocation" - Springer (2005), by A. Meucci for the theory and the routine implemented below See Meucci script for "ComputeMVE.m"

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