PortfolioOptimisers.jl

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Denoise covariance ​

PortfolioOptimisers.DenoiseCovariance Type
julia
struct DenoiseCovariance{T1, T2, T3} <: AbstractCovarianceEstimator
    ce::T1
    denoise::T2
    pdm::T3
    function DenoiseCovariance(ce::AbstractCovarianceEstimator, denoise::Denoise,
                               pdm::Option{<:Posdef})
        return new{typeof(ce), typeof(denoise), typeof(pdm)}(ce, denoise, pdm)
    end
end

A covariance estimator that applies a denoising algorithm and positive definite projection to the output of another covariance estimator. This type enables robust estimation of covariance matrices by first computing a base covariance, then applying denoising and positive definiteness corrections in sequence.

Fields

  • ce: The underlying covariance estimator to be denoised.

  • denoise: The denoising algorithm to apply to the covariance matrix.

  • pdm: The positive definite matrix projection method.

Constructors

julia
DenoiseCovariance(; ce::AbstractCovarianceEstimator; denoise::Denoise = Denoise(),
                  pdm::Option{<:Posdef} = Posdef())

Keyword arguments correspond to the fields above.

Examples

julia
julia> DenoiseCovariance()
DenoiseCovariance
       ce ┼ Covariance
          │    me ┼ SimpleExpectedReturns
          │       │   w ┴ nothing
          │    ce ┼ GeneralCovariance
          │       │   ce ┼ StatsBase.SimpleCovariance: StatsBase.SimpleCovariance(true)
          │       │    w ┴ nothing
          │   alg ┴ Full()
  denoise ┼ Denoise
          │      alg ┼ ShrunkDenoise
          │          │   alpha ┴ Float64: 0.0
          │     args ┼ Tuple{}: ()
          │   kwargs ┼ @NamedTuple{}: NamedTuple()
          │   kernel ┼ typeof(AverageShiftedHistograms.Kernels.gaussian): AverageShiftedHistograms.Kernels.gaussian
          │        m ┼ Int64: 10
          │        n ┼ Int64: 1000
          │      pdm ┼ Posdef
          │          │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton
          │          │   kwargs ┴ @NamedTuple{}: NamedTuple()
      pdm ┼ Posdef
          │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton
          │   kwargs ┴ @NamedTuple{}: NamedTuple()

Related

source
Statistics.cov Method
julia
cov(ce::DenoiseCovariance, X::MatNum; dims = 1, kwargs...)

Compute the denoised and positive definite projected covariance matrix for the data matrix X using the specified DenoiseCovariance estimator.

Arguments

  • ce: The DenoiseCovariance estimator specifying the base covariance estimator, denoising algorithm, and positive definite projection.

  • X: The data matrix (observations × assets).

  • dims: The dimension along which to compute the covariance.

  • kwargs...: Additional keyword arguments passed to the underlying covariance estimator.

Returns

  • sigma::MatNum: denoised covariance matrix.

Validation

  • dims in (1, 2).

Details

  • Computes the covariance matrix using the base estimator in ce.

  • Transposes X if dims == 2 to ensure variables are in columns.

  • Ensures the covariance matrix is mutable.

  • Applies positive definite projection using the method in ce.pdm.

  • Applies the denoising algorithm in ce.denoise with the aspect ratio T/N.

  • Returns the processed covariance matrix.

Related

source
Statistics.cor Method
julia
cor(ce::DenoiseCovariance, X::MatNum; dims = 1, kwargs...)

Compute the denoised and positive definite projected correlation matrix for the data matrix X using the specified DenoiseCovariance estimator.

Arguments

  • ce: The DenoiseCovariance estimator specifying the base covariance estimator, denoising algorithm, and positive definite projection.

  • X: The data matrix (observations × assets).

  • dims: The dimension along which to compute the correlation.

  • kwargs...: Additional keyword arguments passed to the underlying correlation estimator.

Returns

  • rho::MatNum: denoised correlation matrix.

Validation

  • dims in (1, 2).

Details

  • Computes the correlation matrix using the base estimator in ce.

  • Transposes X if dims == 2 to ensure variables are in columns.

  • Ensures the correlation matrix is mutable.

  • Applies positive definite projection using the method in ce.pdm.

  • Applies the denoising algorithm in ce.denoise with the aspect ratio T/N.

  • Returns the processed correlation matrix.

Related

source