Coskewness

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

Abstract supertype for all coskewness estimators in PortfolioOptimisers.jl.

All concrete types implementing coskewness estimation algorithms should subtype CoskewnessEstimator. This enables a consistent interface for coskewness-based higher moment estimators throughout the package.

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PortfolioOptimisers.Coskewness — Type
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. This enables modular workflows for higher-moment portfolio analysis.

Fields

  • me::AbstractExpectedReturnsEstimator: Mean estimator for expected returns.
  • mp::AbstractMatrixProcessingEstimator: Matrix processing estimator for coskewness tensors.
  • alg::AbstractMomentAlgorithm: Moment algorithm (e.g., Full, Semi).

Constructor

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

Construct a Coskewness estimator with the specified mean estimator, matrix processing estimator, and moment algorithm.

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PortfolioOptimisers.Coskewness — Method
Coskewness(; me::AbstractExpectedReturnsEstimator = SimpleExpectedReturns(),
            mp::AbstractMatrixProcessingEstimator = NonPositiveDefiniteMatrixProcessing(),
            alg::AbstractMomentAlgorithm = Full())

Construct a Coskewness estimator for coskewness computation.

Arguments

  • me::AbstractExpectedReturnsEstimator: Mean estimator for expected returns.
  • mp::AbstractMatrixProcessingEstimator: Matrix processing estimator.
  • alg::AbstractMomentAlgorithm: Moment algorithm.

ReturnsResult

  • Coskewness: Configured coskewness estimator.

Examples

julia> Coskewness()
Coskewness
   me | SimpleExpectedReturns
      |   w | nothing
   mp | NonPositiveDefiniteMatrixProcessing
      |   denoise | nothing
      |    detone | nothing
      |       alg | nothing
  alg | Full()

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PortfolioOptimisers.__coskewness — Function
__coskewness(cskew::AbstractMatrix, X::AbstractMatrix, mp::AbstractMatrixProcessingEstimator)

Internal helper for coskewness matrix processing.

__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::AbstractMatrix: Coskewness tensor (flattened or block matrix).
  • X::AbstractMatrix: Data matrix (observations × assets).
  • mp::AbstractMatrixProcessingEstimator: Matrix processing estimator.

ReturnsResult

  • V::Matrix: Processed coskewness matrix.

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PortfolioOptimisers._coskewness — Function
_coskewness(y::AbstractMatrix, X::AbstractMatrix, mp::AbstractMatrixProcessingEstimator)

Internal helper for coskewness computation.

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

Arguments

  • y::AbstractMatrix: Centered data vector (e.g., X .- mean).
  • X::AbstractMatrix: Data matrix (observations × assets).
  • mp::AbstractMatrixProcessingEstimator: Matrix processing estimator.

ReturnsResult

  • cskew::Matrix: Coskewness tensor.
  • V::Matrix: Processed coskewness matrix.

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PortfolioOptimisers.coskewness — Function
coskewness(ske::Coskewness{<:Any, <:Any, <:Full}, X::AbstractMatrix; dims::Int = 1, mean = nothing, kwargs...)
coskewness(ske::Coskewness{<:Any, <:Any, <:Semi}, X::AbstractMatrix; dims::Int = 1, mean = nothing, kwargs...)
coskewness(::Nothing, args...; 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{<:Any, <:Any, <:Full}: Coskewness estimator with Full moment algorithm.
  • ske::Coskewness{<:Any, <:Any, <:Semi}: Coskewness estimator with Semi moment algorithm.
  • ske::Nothing: No-op coskewness computation, returns (nothing, nothing).
  • X::AbstractMatrix: Data matrix (observations × assets).
  • dims::Int: Dimension along which to compute the mean.
  • mean: Optional mean vector. If not provided, computed using the estimator's mean estimator.
  • kwargs...: Additional keyword arguments passed to the mean estimator.

ReturnsResult

  • cskew::Matrix: Coskewness tensor (observations × assets^2).
  • V::Matrix: Processed coskewness matrix (assets × assets).

Examples

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}:
 -0.456556   0.104588   0.391789  …   0.391789  -0.283963   0.025956
 -0.136453  -0.191539  -0.139315     -0.139315   0.210037  -0.0952308
  0.176565  -0.219895   0.24526       0.24526    0.105632  -0.772302

julia> V
3×3 Matrix{Float64}:
 0.74159    0.428314   0.0676831
 0.428314   0.316494   0.0754933
 0.0676831  0.0754933  0.833249

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