Mutual Information Covariance

PortfolioOptimisers.MutualInfoCovariance Type

struct MutualInfoCovariance{T1, T2, T3} <: AbstractCovarianceEstimator
    ve::T1
    bins::T2
    normalise::T3
end

Covariance estimator based on mutual information.

MutualInfoCovariance implements a robust covariance estimator that uses mutual information (MI) to capture both linear and nonlinear dependencies between asset returns. This estimator is particularly useful for identifying complex relationships that are not detected by traditional correlation-based methods. The MI matrix is optionally normalised and then rescaled by marginal standard deviations to produce a covariance matrix.

Fields

• ve: Variance estimator used to compute marginal standard deviations.

• bins: Binning algorithm or fixed number of bins for histogram-based MI estimation.

• normalise: Whether to normalise the MI matrix.

Constructor

MutualInfoCovariance(; ve::AbstractVarianceEstimator = SimpleVariance(),
                     bins::Union{<:AbstractBins, <:Integer} = HacineGharbiRavier(),
                     normalise::Bool = true)

Keyword arguments correspond to the fields above.

Validation

• If bins is an integer, bins > 0.

Examples

julia> MutualInfoCovariance()
MutualInfoCovariance
         ve ┼ SimpleVariance
            │          me ┼ SimpleExpectedReturns
            │             │   w ┴ nothing
            │           w ┼ nothing
            │   corrected ┴ Bool: true
       bins ┼ HacineGharbiRavier()
  normalise ┴ Bool: true

Related

• AbstractVarianceEstimator

• AbstractBins

source

Statistics.cov Method

cov(ce::MutualInfoCovariance, X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute the mutual information (MI) covariance matrix using a MutualInfoCovariance estimator.

This method computes the pairwise mutual information covariance matrix for the input data matrix X, using the binning strategy and normalisation specified in ce. The MI covariance matrix is obtained by rescaling the MI correlation matrix by the marginal standard deviations, as estimated by the variance estimator in ce.

Arguments

• ce: Mutual information-based covariance estimator.

• X: Data matrix of asset returns (observations × assets).

• dims: Dimension along which to compute the covariance.

• kwargs...: Additional keyword arguments passed to the variance estimator.

Returns

• sigma::Matrix{<:Real}: Symmetric matrix of mutual information-based covariances.

Validation

• dims is either 1 or 2.

Examples

Related

• MutualInfoCovariance

• mutual_info

• cor(ce::MutualInfoCovariance, X::AbstractMatrix; dims::Int = 1, kwargs...)

source

Statistics.cor Method

cor(ce::MutualInfoCovariance, X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute the mutual information (MI) correlation matrix using a MutualInfoCovariance estimator.

This method computes the pairwise mutual information correlation matrix for the input data matrix X, using the binning strategy and normalisation specified in ce. The MI correlation captures both linear and nonlinear dependencies between asset returns, making it robust to complex relationships that may not be detected by traditional correlation measures.

Arguments

• ce: Mutual information-based covariance estimator.

• X: Data matrix of asset returns (observations × assets).

• dims: Dimension along which to compute the correlation.

• kwargs...: Additional keyword arguments (currently unused).

Returns

• rho::Matrix{<:Real}: Symmetric matrix of mutual information-based correlation coefficients.

Validation

• dims is either 1 or 2.

Related

• MutualInfoCovariance

• mutual_info

• cov(ce::MutualInfoCovariance, X::AbstractMatrix; dims::Int = 1, kwargs...)

source