Detone

PortfolioOptimisers.Detone — Type
struct Detone{T1} <: AbstractDetoneEstimator
    n::T1
end

A concrete detoning estimator for removing the top n principal components (market modes) from a covariance or correlation matrix.

Fields

  • n::Integer: Number of leading principal components to remove.

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PortfolioOptimisers.Detone — Method
Detone(; n::Integer = 1)

Construct a Detone estimator for removing the top n principal components (market modes) from a covariance or correlation matrix.

Arguments

  • n::Integer: Number of leading principal components to remove. Must satisfy n ≥ 0.

ReturnsResult

  • Detone: A detoning estimator.

Examples

julia> dt = Detone(; n = 2)
Detone
  n | Int64: 2

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PortfolioOptimisers.detone! — Function
detone!(dt::Detone, X::AbstractMatrix, pdm::Union{Nothing, <:Posdef} = Posdef())
detone!(::Nothing, args...)

In-place removal of the top n principal components (market modes) from a covariance or correlation matrix.

  • If dt is nothing, this is a no-op and returns nothing.
  • If dt is a Detone object, the top n principal components are removed from X in-place. Optionally, a Posdef can be provided to ensure the output is positive definite.

Arguments

  • dt::Detone: The detoning estimator specifying the number of components to remove.
  • X::AbstractMatrix: The covariance or correlation matrix to be detoned (modified in-place).
  • pdm::Union{Nothing, <:Posdef}: Optional positive definite matrix estimator.

ReturnsResult

  • nothing. The input matrix X is modified in-place.

Validation

  • If X is a covariance matrix, it is internally converted to a correlation matrix for detoning and then rescaled.
  • The number of components removed is validated to be within the matrix size.
  • If pdm is provided, the result is projected to the nearest positive definite matrix.

Examples

julia> using StableRNGs

julia> rng = StableRNG(123456789);

julia> X = rand(rng, 10, 5);

julia> X = X' * X
5×5 Matrix{Float64}:
 3.29494  2.0765   1.73334  2.01524  1.77493
 2.0765   2.46967  1.39953  1.97242  2.07886
 1.73334  1.39953  1.90712  1.17071  1.30459
 2.01524  1.97242  1.17071  2.24818  1.87091
 1.77493  2.07886  1.30459  1.87091  2.44414

julia> detone!(Detone(), X)

julia> X
5×5 Matrix{Float64}:
  3.29494    -1.14673     0.0868439  -0.502106   -1.71581
 -1.14673     2.46967    -0.876289   -0.0864304   0.274663
  0.0868439  -0.876289    1.90712    -1.18851    -0.750345
 -0.502106   -0.0864304  -1.18851     2.24818    -0.0774753
 -1.71581     0.274663   -0.750345   -0.0774753   2.44414

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PortfolioOptimisers.detone — Function
detone(dt::Detone, X::AbstractMatrix, pdm::Union{Nothing, <:Posdef} = Posdef())
detone(::Nothing, args...)

Same as detone!, but returns a new matrix instead of modifying X in-place.

  • If dt is nothing, this is a no-op and returns nothing.

Examples

julia> using StableRNGs

julia> rng = StableRNG(123456789);

julia> X = rand(rng, 10, 5);

julia> X = X' * X
5×5 Matrix{Float64}:
 3.29494  2.0765   1.73334  2.01524  1.77493
 2.0765   2.46967  1.39953  1.97242  2.07886
 1.73334  1.39953  1.90712  1.17071  1.30459
 2.01524  1.97242  1.17071  2.24818  1.87091
 1.77493  2.07886  1.30459  1.87091  2.44414

julia> Xd = detone(Detone(), X)
5×5 Matrix{Float64}:
  3.29494    -1.14673     0.0868439  -0.502106   -1.71581
 -1.14673     2.46967    -0.876289   -0.0864304   0.274663
  0.0868439  -0.876289    1.90712    -1.18851    -0.750345
 -0.502106   -0.0864304  -1.18851     2.24818    -0.0774753
 -1.71581     0.274663   -0.750345   -0.0774753   2.44414

Related

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PortfolioOptimisers.AbstractDetoneEstimator — Type

abstract type AbstractDetoneEstimator <: AbstractEstimator end

Abstract supertype for all detoning estimators in PortfolioOptimisers.jl.

All concrete types representing detoning estimators (such as Detone) should subtype AbstractDetoneEstimator. This enables a consistent interface for detoning routines and downstream analysis.

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