Matrix processing

Co-moment matrices can be post-processed after being computed. These processes are often complementary but there is no set order.

At the base level, we have four possible post processing steps:

Positive definite projection.
Denoising.
Detoning.
Custom process.

The only set order is that positive definite projection should come first. This is because the other post-processing methods work best with positive definite matrices, and may use positive definite projection internally.

Aside from this, there is no set canonical order, the closest to a heuristic we can justify is to denoise before detoning. As such we provide all permutations of ordering for the last three steps.

PortfolioOptimisers.AbstractMatrixProcessingEstimator Type

julia

abstract type AbstractMatrixProcessingEstimator <: AbstractEstimator end

Abstract supertype for all matrix processing estimator types in PortfolioOptimisers.jl.

All concrete and/or abstract types that implement matrix processing routines–-such as covariance matrix cleaning, denoising, or detoning–-should be subtypes of AbstractMatrixProcessingEstimator.

Interfaces

In order to implement a new matrix processing estimator which will work seamlessly with the library, subtype AbstractMatrixProcessingEstimator with all necessary parameters as part of the struct, and implement the following methods:

matrix_processing!(mp::AbstractMatrixProcessingEstimator, sigma::MatNum, X::MatNum, args...; kwargs...): In-place processing of a covariance or correlation matrix.
matrix_processing(mp::AbstractMatrixProcessingEstimator, sigma::MatNum, X::MatNum, args...; kwargs...): Optional out-of-place processing of a covariance or correlation matrix.

Arguments

mp: Matrix processing estimator.
sigma: Covariance-like or correlation-like matrix.
X: Data matrix.
args...: Additional positional arguments passed to custom algorithms.
kwargs...: Additional keyword arguments passed to custom algorithms.

Returns

sigma::MatNum: The processed input matrix sigma.

Examples

We can create a dummy matrix processing estimator as follows:

julia

julia> struct MyMatrixProcessingEstimator <: PortfolioOptimisers.AbstractMatrixProcessingEstimator end

julia> function PortfolioOptimisers.matrix_processing!(est::MyMatrixProcessingEstimator,
                                                       sigma::PortfolioOptimisers.MatNum,
                                                       X::PortfolioOptimisers.MatNum)
           # Implement your in-place matrix processing logic here.
           println("Processing matrix in-place...")
           return sigma
       end

julia> function PortfolioOptimisers.matrix_processing(est::MyMatrixProcessingEstimator,
                                                      sigma::PortfolioOptimisers.MatNum,
                                                      X::PortfolioOptimisers.MatNum)
           sigma = copy(sigma)
           println("Copy sigma...")
           matrix_processing!(est, sigma, X)
           return sigma
       end

julia> matrix_processing!(MyMatrixProcessingEstimator(), [1.0 2.0; 2.0 1.0], rand(10, 2))
Processing matrix in-place...
2×2 Matrix{Float64}:
 1.0  2.0
 2.0  1.0

julia> matrix_processing(MyMatrixProcessingEstimator(), [1.0 2.0; 2.0 1.0], rand(10, 2))
Copy sigma...
Processing matrix in-place...
2×2 Matrix{Float64}:
 1.0  2.0
 2.0  1.0

Related

Matrix processing ​

Matrix processing