Quasi-Monte-Carlo algorithm for systematic generation of shock
scenarios from an arbitrary multivariate elliptical distribution. The
algorithm selects a systematic mesh of arbitrary fineness that
approximately evenly covers an isoprobability ellipsoid in d
dimensions.
(Flood, Mark D. & Korenko, George G. “Systematic
Scenario Selection”, Office of Financial Research Working Paper #0005,
2013)
install.packages("devtools")
library(devtools)
install_github("mvk222/SyScSelection")
library(SyScSelection)
Estimate the mean and covariance matrix from the data:
mu <- colMeans(data)
sig <- cov(data)
The number of dimensions, d, is taken directly from the
data:
d <- length(data[1,])
Get the size parameter for a normal dist’n at a 95%
threshold:
calpha <- sizeparam_normal_distn(.95, d)
Create a hyperellipsoid object. Note that the constructor takes
the inverse of the disperion matrix:
hellip <- hyperellipsoid(mu, solve(sig), calpha)
Scenarios are calculated as a mesh of fineness 3. The number of
scenarios is a function of the dimensionality of the hyperellipsoid and
the fineness of the mesh:
scenarios <- hypercube_mesh(3, hellip)
Estimate the mean, covariance, and degrees of freedom from the
data:
mu <- colMeans(data)
sig <- cov(data)
nu <- dim(data)[1] - 1
The number of dimensions, d, is taken directly from the
data:
d <- length(data[1,])
Get the size parameter for a normal dist’n at a 95%
threshold:
calpha <- sizeparam_t_distn(.95, d, nu)
Create a hyperellipsoid object. Note that the constructor takes
the inverse of the disperion matrix:
hellip <- hyperellipsoid(mu, solve(sig), calpha)
Scenarios are calculated as a mesh of fineness 3. The number of
scenarios is a function of the dimensionality of the hyperellipsoid and
the fineness of the mesh:
scenarios <- hypercube_mesh(3, hellip)