make_systems_form

make_systems_form

make_systems_form(
    Phi0::AbstractMatrix, 
    As::Vector{<:AbstractMatrix}, 
    Psis::Vector{<:AbstractMatrix}, 
    Sigma::AbstractMatrix{<:Real}, 
    order::AbstractVector{<:Int}, 
    max_horizon::Int
) -> Tuple{AbstractMatrix, AbstractMatrix}

Transform an SVARMA dynamic model into the systems representation \(x = Bx + Omega\varepsilon\).

Arguments

• Phi0::AbstractMatrix: The matrix of contemporaneous structural impulse responses.
• As::Vector{<:AbstractMatrix}: A vector of reduced-form autoregressive (AR). First entry corresponds to the AR matrix for the first lag, etc.
• Psis::Vector{<:AbstractMatrix}: A vector of reduced-form moving average (MA) matrices. First index corresponds to the first lag, etc.
• Sigma::AbstractMatrix{<:Real}: The covariance matrix of reduced-form errors.
• order::AbstractVector{<:Int}: The vector indicating the order of variables, typically determined by the transmission matrix.
• max_horizon::Int: The maximum time horizon to consider for the systems model, with 0 representing the contemporaneous period.

Returns

• (B, Omega) with the meaning being the same as in Wegner et al (2024).

Notes

• Use make_B and make_Omega to construct the two matrices seperately.