Description Usage Arguments Details Value Author(s) References
Function computes the minimum volume ellipsoid for a given time series
1 |
data |
a matrix time-series of data. Each row is a observation (date). Each column is an asset |
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
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
Ram Ahluwalia ram@wingedfootcapital.com
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"
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