Coskewness

julia

struct Coskewness{__T_me, __T_mp, __T_alg} <: CoskewnessEstimator

Container type for coskewness estimators.

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

Fields

me: Expected returns estimator.
mp: Matrix processing estimator.
alg: Moment algorithm.

Constructors

julia

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

Keywords correspond to the struct's fields.

Examples

julia

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

Related

source

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: Dimension 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

source

julia

coskewness(ske::WindowedCoskewness, X::MatNum; dims::Int = 1, iv::Option{<:MatNum} = nothing, kwargs...)

Compute the coskewness tensor and processed matrix using a rolling or indexed observation window.

This method selects a window of observations from X (and applies observation weights if specified), then delegates to the underlying coskewness estimator.

Arguments

ske: Windowed coskewness estimator.
X: Data matrix of asset returns (observations × assets).
dims: Dimension along which to perform the computation.
iv: Optional implied volatility matrix. Used if any internal covariance estimator is an instance of ImpliedVolatility.
kwargs...: Additional keyword arguments passed to the underlying estimator.

Returns

cskew::Matrix{<:Number}: Coskewness tensor (assets × assets²).
V::Matrix{<:Number}: Processed coskewness matrix (assets × assets).

Related

source

PortfolioOptimisers.CoskewnessEstimator Type

julia

abstract type CoskewnessEstimator <: AbstractEstimator

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

source

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

source

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

Coskewness ​

Coskewness