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Denoise covariance

PortfolioOptimisers.DenoiseCovariance — Function
DenoiseCovariance(;
    ce::StatsBase.CovarianceEstimator = Covariance(),
    dn::AbstractDenoiseEstimator = Denoise(),
    pdm::Option{<:AbstractPosdefEstimator} = Posdef(),
) -> PortfolioOptimisersCovariance

DenoiseCovariance(
    ce::StatsBase.CovarianceEstimator,
    dn::AbstractDenoiseEstimator,
    pdm::Option{<:AbstractPosdefEstimator},
) -> PortfolioOptimisersCovariance

Convenience constructor. Returns a PortfolioOptimisersCovariance configured to apply positive definite projection then denoising, in that order, via MatrixProcessing.

denoise! in src/04_MatrixProcessing/02_Denoise.jl states the mathematics of the denoising step, and posdef! in src/04_MatrixProcessing/01_PosdefMatrix.jl that of the projection.

Algorithm

  1. Build a MatrixProcessing from pdm and dn, with order = (:pdm, :dn).
  2. Return a PortfolioOptimisersCovariance carrying ce and that estimator.

order is what fixes the composition: Statistics.cov runs ce first, then projects the matrix onto the positive definite cone, and denoises last. A caller who needs the reverse order builds the MatrixProcessing itself.

Arguments

  • ce: Covariance estimator.
  • dn: Matrix denoising estimator.
  • pdm: Optional positive definite matrix estimator.

Returns

  • ce::PortfolioOptimisersCovariance: Composite estimator that denoises the matrix ce computes.

Examples

julia> DenoiseCovariance()PortfolioOptimisersCovariance  ce ┼ Covariance     │    me ┼ SimpleExpectedReturns     │       │   w ┴ nothing     │    ce ┼ GeneralCovariance     │       │   ce ┼ StatsBase.SimpleCovariance: StatsBase.SimpleCovariance(true)     │       │    w ┴ nothing     │   alg ┼ FullMoment()     │     w ┴ nothing  mp ┼ MatrixProcessing     │     pdm ┼ Posdef     │         │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton     │         │   kwargs ┴ @NamedTuple{}: NamedTuple()     │      dn ┼ Denoise     │         │      pdm ┼ Posdef     │         │          │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton     │         │          │   kwargs ┴ @NamedTuple{}: NamedTuple()     │         │      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     │      dt ┼ nothing     │     alg ┼ nothing     │   order ┴ Tuple{Symbol, Symbol}: (:pdm, :dn)

Related

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