PortfolioOptimisers.jl

Appearance

5

Cokurtosis ​

PortfolioOptimisers.Cokurtosis Type
julia
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: Mean estimator for expected returns.

  • mp: Matrix processing estimator for cokurtosis tensors.

  • alg: Moment algorithm.

Constructor

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

Keyword arguments correspond to the fields above.

Examples

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

Related

source
PortfolioOptimisers.cokurtosis Function
julia
cokurtosis(ke::Union{Nothing, <:Cokurtosis}, X::AbstractMatrix; dims::Int = 1,
           mean = nothing, 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 estimator.

    • 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, returns nothing.

  • X: Data matrix (observations × assets).

  • dims: 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.

Validation

  • dims is either 1 or 2.

Returns

  • ckurt::Matrix{<:Real}: Cokurtosis tensor (assets^2 × assets^2).

Examples

julia
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

Related

source
PortfolioOptimisers.CokurtosisEstimator Type
julia
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.

Related

source
PortfolioOptimisers._cokurtosis Function
julia
_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: Data matrix (observations × assets).

  • mp: Matrix processing estimator.

Returns

  • ckurt::Matrix{<:Real}: Cokurtosis tensor after matrix processing.

Related

source