Distance

PortfolioOptimisers.Distance Type

struct Distance{T1, T2} <: AbstractDistanceEstimator
    power::T1
    alg::T2
end

If power is not nothing, computes the generalised distance estimator.

$$\begin{array}{rl}{}_g{d}_{i,j}& =s\cdot {\left(d_{i,j}\right)}^p\\ s& =\{\begin{array}{ll}1/2& \text{if }p\mathrm{mod}2\ne 0\\ 1& \text{otherwise}\end{array},\end{array}$$

where ${}_{g}d$ is the generalised distance, $d$ is the base distance computed using the specified distance algorithm, $p$ is the integer power, $s$ is a scaling factor, and each subscript denotes an asset.

Fields

• power: Optional integer power to which the base correlation or distance matrix is raised.

• alg: The base distance algorithm.

Constructor

Distance(; power::Union{Nothing, <:Integer} = nothing,
         alg::AbstractDistanceAlgorithm = SimpleDistance())

Keyword arguments correspond to the fields above.

Validation

• If power is not nothing, then power >= 1.

Examples

julia> Distance()
Distance
  power ┼ nothing
    alg ┴ SimpleDistance()

Related

• distance

• cor_and_dist

• SimpleDistance

• SimpleAbsoluteDistance

• LogDistance

• CorrelationDistance

• CanonicalDistance

• VariationInfoDistance

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PortfolioOptimisers.distance Method

distance(de::Distance{<:Any,
                      <:Union{<:SimpleDistance, <:SimpleAbsoluteDistance, <:LogDistance,
                              <:CorrelationDistance, <:CanonicalDistance}},
         ce::StatsBase.CovarianceEstimator, X::AbstractMatrix; dims::Int = 1, kwargs...)

This method computes the correlation matrix using the provided covariance estimator ce and data matrix X, which is used to compute the distance matrix based on the specified distance algorithm in de.

Arguments

• de: Distance estimator.

  • de::Distance{<:Any, <:SimpleDistance}: Use the SimpleDistance algorithm.

  • de::Distance{<:Any, <:SimpleAbsoluteDistance}: Use the SimpleAbsoluteDistance algorithm.

  • de::Distance{<:Any, <:LogDistance}: Use the LogDistance algorithm.

  • de::Distance{<:Any, <:CorrelationDistance}: Use the CorrelationDistance algorithm.

  • de::Distance{<:Any, <:CanonicalDistance}: Use the CanonicalDistance algorithm.

• ce: Covariance estimator.

• X: Data matrix (observations × features).

• dims: Dimension along which to compute the correlation.

• kwargs...: Additional keyword arguments passed to the correlation computation.

Returns

• dist::Matrix{<:Real}: Matrix of pairwise distances.

Related

• Distance

• SimpleDistance

• SimpleAbsoluteDistance

• LogDistance

• CorrelationDistance

• CanonicalDistance

• cor_and_dist

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PortfolioOptimisers.distance Method

distance(de::Distance{<:Any, <:LogDistance},
         ce::Union{<:LowerTailDependenceCovariance,
                   <:PortfolioOptimisersCovariance{<:LowerTailDependenceCovariance, <:Any}},
         X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute the log-distance matrix from a Lower Tail Dependence (LTD) covariance estimator and data matrix.

Arguments

• de::Distance{<:Any, <:LogDistance}: Distance estimator with LogDistance algorithm.

• ce: LTD covariance estimator or a PortfolioOptimisersCovariance wrapping an LTD estimator.

• X: Data matrix (observations × features).

• dims: Dimension along which to compute the correlation.

• kwargs...: Additional keyword arguments passed to the correlation computation.

Returns

• dist::Matrix{<:Real}: Matrix of pairwise log-distances.

Related

• Distance

• LogDistance

• cor_and_dist

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PortfolioOptimisers.distance Method

distance(de::Distance{<:Any, <:VariationInfoDistance}, ::Any, X::AbstractMatrix;
         dims::Int = 1, kwargs...)

Compute the variation of information (VI) distance matrix from a data matrix.

Arguments

• de::Distance{<:Any, <:VariationInfoDistance}: Distance estimator with VariationInfoDistance algorithm.

• ::Any: Covariance estimator placeholder for API compatibility (ignored).

• X: Data matrix (observations × features).

• dims: Dimension along which to compute the distance. If 2, the data is transposed.

• kwargs...: Additional keyword arguments (ignored).

Validation

• dims is either 1 or 2.

Returns

• dist::Matrix{<:Real}: Matrix of pairwise variation of information distances.

Details

• The number of bins and normalisation are taken from the VariationInfoDistance algorithm fields.

• If dims == 2, the data matrix is transposed before computation.

Related

• Distance

• VariationInfoDistance

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PortfolioOptimisers.distance Method

distance(::Distance{<:Any,
                    <:Union{<:SimpleDistance, <:SimpleAbsoluteDistance, <:LogDistance,
                            <:CorrelationDistance, <:CanonicalDistance}},
         rho::AbstractMatrix, args...; kwargs...)

Compute the distance matrix from a correlation or covariance matrix.

If the input rho is a covariance matrix, it is converted to a correlation matrix which is used to compute the distance matrix using the specified distance algorithm in de.

Arguments

• de: Distance estimator.

  • de::Distance{<:Any, <:SimpleDistance}: Use the SimpleDistance algorithm.

  • de::Distance{<:Any, <:SimpleAbsoluteDistance}: Use the SimpleAbsoluteDistance algorithm.

  • de::Distance{<:Any, <:LogDistance}: Use the LogDistance algorithm.

  • de::Distance{<:Any, <:CorrelationDistance}: Use the CorrelationDistance algorithm.

  • de::Distance{<:Any, <:CanonicalDistance}: Use the CanonicalDistance algorithm.

• rho: Correlation or covariance matrix.

• args...: Additional arguments (ignored).

• kwargs...: Additional keyword arguments.

Returns

• dist::Matrix{<:Real}: Matrix of pairwise Euclidean distances.

Details

• If rho is a covariance matrix, it is converted to a correlation matrix using StatsBase.cov2cor.

Related

• Distance

• SimpleDistance

• SimpleAbsoluteDistance

• LogDistance

• CorrelationDistance

• CanonicalDistance

• cor_and_dist

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PortfolioOptimisers.cor_and_dist Method

cor_and_dist(de::Distance{<:Any,
                          <:Union{<:SimpleDistance, <:SimpleAbsoluteDistance, <:LogDistance,
                                  <:LogDistance, <:VariationInfoDistance,
                                  <:CorrelationDistance}}, Nothing,
             ce::StatsBase.CovarianceEstimator, X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute and return the correlation and distance matrices. The distance matrix depends on the combination of distance and covariance estimators (see distance).

Arguments

• de: Distance estimator.

• ce: Covariance estimator.

• X: Data matrix (observations × features).

• dims: Dimension along which to compute the correlation.

• kwargs...: Additional keyword arguments passed to the correlation computation.

Validation

• dims in (1, 2).

Returns

• (rho::Matrix{<:Real}, dist::Matrix{<:Real}): Tuple of correlation matrix and distance matrix.

Related

• Distance

• distance

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PortfolioOptimisers.distance Method

distance(de::Distance{<:Any, <:CanonicalDistance},
         ce::Union{<:MutualInfoCovariance,
                   <:PortfolioOptimisersCovariance{<:MutualInfoCovariance, <:Any},
                   <:LowerTailDependenceCovariance, <:PortfolioOptimisersCovariance{<:LowerTailDependenceCovariance, <:Any},
                   <:DistanceCovariance,
                   <:PortfolioOptimisersCovariance{<:DistanceCovariance, <:Any}},
         X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute the canonical distance matrix using the covariance estimator and data matrix. The method selects the appropriate distance algorithm based on the type of covariance estimator provided (see CanonicalDistance).

Arguments

• de::Distance{<:Any, <:CanonicalDistance}: Distance estimator using the CanonicalDistance algorithm.

• ce::MutualInfoCovariance: Mutual information covariance estimator.

• X: Data matrix (observations × features).

• dims: Dimension along which to compute the distance.

• kwargs...: Additional keyword arguments.

Returns

• dist::Matrix{<:Real}: Matrix of pairwise canonical distances.

Related

• Distance

• CanonicalDistance

• MutualInfoCovariance

• LowerTailDependenceCovariance

• DistanceCovariance

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