adknudson / RandomCorrelationMatrices.jl

Functions to generate random correlation matrices

RandomCorrelationMatrices

Generate random correlation matrices, for some definition of random. Currently supports just one definition/method:

Lewandowski, Daniel, Dorota Kurowicka, and Harry Joe. "Generating random correlation matrices based on vines and extended onion method." Journal of multivariate analysis 100.9 (2009): 1989-2001. doi:10.1016/j.jmva.2009.04.008

This package has two functions, randcormatrix(d, η) and randcovmatrix(d, η, σ) . d is the dimension, and η is a parameter that controls the distribution of the off-diagonal terms. randcovmatrix is used to generate a covariance matrix from the output of randcormatrix, where the standard deviation of each component is controlled by σ.

Example Usage

To get a feel for how to set η, consider the following output, which shows some example matrices and the average range of off-diagonals:

julia> using Statistics, LinearAlgebra

julia> n = 4; η = 2;

julia> r = randcormatrix(n, η)
4×4 Matrix{Float64}:
  1.0        0.58787   0.27138   -0.105909
  0.58787    1.0       0.281755  -0.107723
  0.27138    0.281755  1.0        0.249834
 -0.105909  -0.107723  0.249834   1.0

julia> ranges = zeros(Float64, 1000);

julia> for i in eachindex(ranges)
           r = randcormatrix(n, η)
           r0 = r - Diagonal(r) # gets rid of diagonal elements which are all 1's
           ranges[i] = maximum(r0) - minimum(r0)
        end;

julia> mean(ranges)
0.9431632935736379

julia> median(ranges)
0.944170516935672

julia> η = 32
32

julia> ranges = zeros(Float64, 1000);

julia> for i in eachindex(ranges)
           r = randcormatrix(n, η)
           r0 = r - Diagonal(r) # gets rid of diagonal elements which are all 1's
           ranges[i] = maximum(r0) - minimum(r0)
        end;

julia> mean(ranges)
0.3116603248881609

julia> median(ranges)
0.3087574323261617

Below is an example showing how to generate a covariance matrix

julia> σ = [100, 200, 300, 400, 500];

julia> n = length(σ)
5

julia> η = 10;

julia> randcovmatrix(n, η, σ)
5×5 Matrix{Float64}:
 10000.0    -3506.58    5461.39   16673.6    -1129.93
 -3506.58   40000.0   -11972.9    -6078.8   -13199.7
  5461.39  -11972.9    90000.0    -6982.46  -10392.4
 16673.6    -6078.8    -6982.46  160000.0    57847.9
 -1129.93  -13199.7   -10392.4    57847.9   250000.0

Contributing

Pull requests welcome for additional methods of generating random correlation matrices that are described in the literature.