Rank Covariances

PortfolioOptimisers.RankCovarianceEstimator — Type
abstract type RankCovarianceEstimator <: AbstractCovarianceEstimator end

Abstract supertype for all rank-based covariance estimators in PortfolioOptimisers.jl.

All concrete types implementing rank-based covariance estimation algorithms (such as Kendall's tau or Spearman's rho) should subtype RankCovarianceEstimator. This enables a consistent interface for rank-based covariance estimators throughout the package and allows for flexible extension and dispatch.

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PortfolioOptimisers.KendallCovariance — Type
struct KendallCovariance{T1} <: RankCovarianceEstimator

Robust covariance estimator based on Kendall's tau rank correlation.

KendallCovariance implements a covariance estimator that uses Kendall's tau rank correlation to measure the monotonic association between pairs of asset returns. This estimator is robust to outliers and non-Gaussian data, making it suitable for financial applications where heavy tails or non-linear dependencies are present.

Fields

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

Constructor

KendallCovariance(; ve::AbstractVarianceEstimator = SimpleVariance())

Construct a KendallCovariance object with the specified variance estimator.

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PortfolioOptimisers.KendallCovariance — Method
KendallCovariance(; ve::AbstractVarianceEstimator = SimpleVariance())

Construct a KendallCovariance estimator for robust rank-based covariance or correlation estimation using Kendall's tau.

This constructor creates a KendallCovariance object using the specified variance estimator. The estimator computes the covariance matrix by combining the Kendall's tau rank correlation matrix with the marginal standard deviations.

Arguments

  • ve::AbstractVarianceEstimator: Variance estimator.

ReturnsResult

  • KendallCovariance: A configured Kendall's tau-based covariance estimator.

Examples

julia> ce = KendallCovariance()
KendallCovariance
  ve | SimpleVariance
     |          me | SimpleExpectedReturns
     |             |   w | nothing
     |           w | nothing
     |   corrected | Bool: true

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Statistics.cor — Method
cor(::KendallCovariance, X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute the Kendall's tau rank correlation matrix using a KendallCovariance estimator.

This method computes the pairwise Kendall's tau rank correlation matrix for the input data matrix X. Kendall's tau measures the monotonic association between pairs of asset returns and is robust to outliers and non-Gaussian data.

Arguments

  • ce::KendallCovariance: Kendall's tau-based covariance estimator.
  • X::AbstractMatrix: Data matrix of asset returns (observations × assets).
  • dims::Int: Dimension along which to compute the correlation.
  • kwargs...: Additional keyword arguments (currently unused).

ReturnsResult

  • rho::Matrix{Float64}: Symmetric matrix of Kendall's tau rank correlation coefficients.

Validation

  • Asserts that dims is either 1 or 2.

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Statistics.cov — Method
cov(ce::KendallCovariance, X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute the Kendall's tau rank covariance matrix using a KendallCovariance estimator.

This method computes the covariance matrix for the input data matrix X by combining the Kendall's tau rank correlation matrix with the marginal standard deviations estimated by the variance estimator in ce. This approach is robust to outliers and non-Gaussian data.

Arguments

  • ce::KendallCovariance: Kendall's tau-based covariance estimator.
  • X::AbstractMatrix: Data matrix of asset returns (observations × assets).
  • dims::Int: Dimension along which to compute the covariance.
  • kwargs...: Additional keyword arguments passed to the variance estimator.

ReturnsResult

  • sigma::Matrix{Float64}: Symmetric matrix of Kendall's tau rank covariances.

Validation

  • Asserts that dims is either 1 or 2.

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PortfolioOptimisers.SpearmanCovariance — Type
struct SpearmanCovariance{T1} <: RankCovarianceEstimator

Robust covariance estimator based on Spearman's rho rank correlation.

SpearmanCovariance implements a covariance estimator that uses Spearman's rho rank correlation to measure the monotonic association between pairs of asset returns. This estimator is robust to outliers and non-Gaussian data, making it suitable for financial applications where heavy tails or non-linear dependencies are present.

Fields

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

Constructor

SpearmanCovariance(; ve::AbstractVarianceEstimator = SimpleVariance())

Construct a SpearmanCovariance object with the specified variance estimator.

Related

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PortfolioOptimisers.SpearmanCovariance — Method
SpearmanCovariance(; ve::AbstractVarianceEstimator = SimpleVariance())

Construct a SpearmanCovariance estimator for robust rank-based covariance or correlation estimation using Spearman's rho.

This constructor creates a SpearmanCovariance object using the specified variance estimator. The estimator computes the covariance matrix by combining the Spearman's rho rank correlation matrix with the marginal standard deviations.

Arguments

  • ve::AbstractVarianceEstimator: Variance estimator.

ReturnsResult

  • SpearmanCovariance: A configured Spearman's rho-based covariance estimator.

Examples

julia> ce = SpearmanCovariance()
SpearmanCovariance
  ve | SimpleVariance
     |          me | SimpleExpectedReturns
     |             |   w | nothing
     |           w | nothing
     |   corrected | Bool: true

Related

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Statistics.cor — Method
cor(::SpearmanCovariance, X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute the Spearman's rho rank correlation matrix using a SpearmanCovariance estimator.

This method computes the pairwise Spearman's rho rank correlation matrix for the input data matrix X. Spearman's rho measures the monotonic association between pairs of asset returns and is robust to outliers and non-Gaussian data.

Arguments

  • ce::SpearmanCovariance: Spearman's rho-based covariance estimator.
  • X::AbstractMatrix: Data matrix of asset returns (observations × assets).
  • dims::Int: Dimension along which to compute the correlation (1 = columns/assets, 2 = rows). Default is 1.
  • kwargs...: Additional keyword arguments (currently unused).

ReturnsResult

  • rho::Matrix{Float64}: Symmetric matrix of Spearman's rho rank correlation coefficients.

Validation

  • Asserts that dims is either 1 or 2.

Related

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Statistics.cov — Method
cov(ce::SpearmanCovariance, X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute the Spearman's rho rank covariance matrix using a SpearmanCovariance estimator.

This method computes the covariance matrix for the input data matrix X by combining the Spearman's rho rank correlation matrix with the marginal standard deviations estimated by the variance estimator in ce. This approach is robust to outliers and non-Gaussian data.

Arguments

  • ce::SpearmanCovariance: Spearman's rho-based covariance estimator.
  • X::AbstractMatrix: Data matrix of asset returns (observations × assets).
  • dims::Int: Dimension along which to compute the covariance (1 = columns/assets, 2 = rows). Default is 1.
  • kwargs...: Additional keyword arguments passed to the variance estimator.

ReturnsResult

  • sigma::Matrix{Float64}: Symmetric matrix of Spearman's rho rank covariances.

Validation

  • Asserts that dims is either 1 or 2.

Related

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