PortfolioOptimisers.jl

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Coskewness ​

PortfolioOptimisers.Coskewness Type
julia
struct Coskewness{T1, T2, T3} <: CoskewnessEstimator
    me::T1
    mp::T2
    alg::T3
end

Container type for coskewness estimators.

Coskewness encapsulates the mean estimator, matrix processing estimator, and moment algorithm for coskewness estimation.

Fields

  • me: Mean estimator for expected returns.

  • mp: Matrix processing estimator for coskewness tensors.

  • alg: Moment algorithm.

Constructor

julia
Coskewness(; me::AbstractExpectedReturnsEstimator = SimpleExpectedReturns(),
           mp::AbstractMatrixProcessingEstimator = DenoiseDetoneAlgMatrixProcessing(),
           alg::AbstractMomentAlgorithm = Full())

Keyword arguments correspond to the fields above.

Examples

julia
julia> Coskewness()
Coskewness
   me ┼ SimpleExpectedReturns
      │     w ┼ nothing
      │   idx ┴ nothing
   mp ┼ DenoiseDetoneAlgMatrixProcessing
      │     pdm ┼ Posdef
      │         │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton
      │         │   kwargs ┴ @NamedTuple{}: NamedTuple()
      │      dn ┼ nothing
      │      dt ┼ nothing
      │     alg ┼ nothing
      │   order ┴ DenoiseDetoneAlg()
  alg ┴ Full()

Related

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PortfolioOptimisers.coskewness Function
julia
coskewness(ske::Option{<:Coskewness}, X::MatNum; dims::Int = 1,
           mean = nothing, kwargs...)

Compute the full coskewness tensor and processed matrix for a dataset. For Full, it uses all centered data; for Semi, it uses only negative deviations. If the estimator is nothing, returns (nothing, nothing).

Arguments

  • ske: Coskewness estimator.

    • ske::Coskewness{<:Any, <:Any, <:Full}: Coskewness estimator with Full moment algorithm.

    • ske::Coskewness{<:Any, <:Any, <:Semi}: Coskewness estimator with Semi moment algorithm.

    • ske::Nothing: No-op, returns (nothing, nothing).

  • X: Data matrix (observations × assets).

  • dims: Dimensions along which to perform the computation.

  • mean: Optional mean vector. If not provided, computed using the estimator's mean estimator.

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

Validation

  • dims is either 1 or 2.

Returns

  • cskew::Matrix{<:Number}: Coskewness tensor (observations × assets^2).

  • V::Matrix{<:Number}: Processed coskewness matrix (assets × assets).

Examples

julia
julia> using StableRNGs

julia> rng = StableRNG(123456789);

julia> X = randn(rng, 10, 3);

julia> cskew, V = coskewness(Coskewness(), X);

julia> cskew
3×9 Matrix{Float64}:
 -0.329646    0.0782455   0.325842  …   0.325842  -0.250881   0.16769
  0.0782455  -0.236104   -0.250881     -0.250881   0.266005   0.144546
  0.325842   -0.250881    0.16769       0.16769    0.144546  -0.605589

julia> V
3×3 Matrix{Float64}:
  0.513743   -0.0452078  -0.290893
 -0.0452078   0.402765   -0.0372996
 -0.290893   -0.0372996   0.837701

Related

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PortfolioOptimisers.CoskewnessEstimator Type
julia
abstract type CoskewnessEstimator <: AbstractEstimator end

Abstract supertype for all coskewness estimators in PortfolioOptimisers.jl.

All concrete and/or abstract types implementing coskewness estimation algorithms should be subtypes of CoskewnessEstimator.

Related

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PortfolioOptimisers.negative_spectral_coskewness Function
julia
negative_spectral_coskewness(cskew::MatNum, X::MatNum,
             mp::AbstractMatrixProcessingEstimator)

Internal helper for coskewness matrix processing.

negative_spectral_coskewness processes the coskewness tensor by applying the matrix processing estimator to each block, then projects the result using eigenvalue decomposition and clamps negative values. Used internally for robust coskewness estimation.

Arguments

  • cskew: Coskewness tensor (flattened or block matrix).

  • X: Data matrix (observations × assets).

  • mp: Matrix processing estimator.

Returns

  • V::Matrix{<:Number}: Processed coskewness matrix.

Related

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PortfolioOptimisers._coskewness Function
julia
_coskewness(Y::MatNum, X::MatNum, mp::AbstractMatrixProcessingEstimator)

Internal helper for coskewness computation.

_coskewness computes the coskewness tensor and applies matrix processing. Used internally by coskewness estimators.

Arguments

  • Y: Centered data vector (e.g., X .- mean).

  • X: Data matrix (observations × assets).

  • mp: Matrix processing estimator.

Returns

  • cskew::Matrix{<:Number}: Coskewness tensor.

  • V::Matrix{<:Number}: Processed coskewness matrix.

Related

source