Cokurtosis

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

Abstract supertype for all cokurtosis estimators in PortfolioOptimisers.jl.

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

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PortfolioOptimisers.Cokurtosis — Type
struct Cokurtosis{T1, T2, T3} <: CokurtosisEstimator
    me::T1
    mp::T2
    alg::T3
end

Container type for cokurtosis estimators.

Cokurtosis encapsulates the mean estimator, matrix processing estimator, and moment algorithm for cokurtosis estimation. This enables modular workflows for higher-moment portfolio analysis.

Fields

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

Constructor

Cokurtosis(; me::AbstractExpectedReturnsEstimator = SimpleExpectedReturns(),
            mp::AbstractMatrixProcessingEstimator = DefaultMatrixProcessing(),
            alg::AbstractMomentAlgorithm = Full())

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

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

Construct a Cokurtosis estimator for cokurtosis computation.

Arguments

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

ReturnsResult

  • Cokurtosis: Configured cokurtosis estimator.

Examples

julia> Cokurtosis()
Cokurtosis
   me | SimpleExpectedReturns
      |   w | nothing
   mp | DefaultMatrixProcessing
      |       pdm | Posdef
      |           |   alg | UnionAll: NearestCorrelationMatrix.Newton
      |   denoise | nothing
      |    detone | nothing
      |       alg | nothing
  alg | Full()

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

Internal helper for cokurtosis computation.

_cokurtosis computes the cokurtosis tensor for the input data matrix and applies matrix processing using the specified estimator.

Arguments

  • X::AbstractMatrix: Data matrix (observations × assets).
  • mp::AbstractMatrixProcessingEstimator: Matrix processing estimator.

ReturnsResult

  • ckurt::Matrix: Cokurtosis tensor after matrix processing.

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PortfolioOptimisers.cokurtosis — Function
cokurtosis(ke::Cokurtosis{<:Any, <:Any, <:Full}, X::AbstractMatrix; dims::Int = 1, mean = nothing, kwargs...)
cokurtosis(ke::Cokurtosis{<:Any, <:Any, <:Semi}, X::AbstractMatrix; dims::Int = 1, mean = nothing, kwargs...)
cokurtosis(::Nothing, args...; kwargs...)

Compute the cokurtosis tensor for a dataset.

This method computes the cokurtosis tensor using the estimator's mean and matrix processing algorithm. For Full, it uses all centered data; for Semi, it uses only negative deviations. If the estimator is nothing, returns nothing.

Arguments

  • ke::Cokurtosis{<:Any, <:Any, <:Full}: Cokurtosis estimator with Full moment algorithm.
  • ke::Cokurtosis{<:Any, <:Any, <:Semi}: Cokurtosis estimator with Semi moment algorithm.
  • ke::Nothing: No-op cokurtosis computation, returns 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

  • ckurt::Matrix: Cokurtosis tensor (assets^2 × assets^2).

Examples

julia> using StableRNGs

julia> rng = StableRNG(123456789);

julia> X = randn(rng, 10, 2);

julia> cokurtosis(Cokurtosis(), X)
4×4 Matrix{Float64}:
  1.33947   -0.246726  -0.246726   0.493008
 -0.246726   0.493008   0.493008  -0.201444
 -0.246726   0.493008   0.493008  -0.201444
  0.493008  -0.201444  -0.201444   0.300335

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