change_regime: Change regime parameters *upsilon_{m}* =...

Description Usage Arguments Details Value Warning References

View source: R/parameterReforms.R

Description

change_regime changes the regime parameters (excluding mixing weights parameter) of the pointed regime to the new given parameters.

Usage

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change_regime(
  p,
  M,
  d,
  params,
  model = c("GMVAR", "StMVAR", "G-StMVAR"),
  m,
  regime_pars,
  structural_pars = NULL
)

Arguments

p

a positive integer specifying the autoregressive order of the model.

M
For GMVAR and StMVAR models:

a positive integer specifying the number of mixture components.

For G-StMVAR models:

a size (2x1) integer vector specifying the number of GMVAR type components M1 in the first element and StMVAR type components M2 in the second element. The total number of mixture components is M=M1+M2.

d

number of time series in the system, i.e. the dimension.

params

a real valued vector specifying the parameter values.

For unconstrained models:

Should be size ((M(pd^2+d+d(d+1)/2+2)-M1-1)x1) and have the form θ = (υ_{1}, ...,υ_{M}, α_{1},...,α_{M-1},ν), where

  • υ_{m} = (φ_{m,0},φ_{m},σ_{m})

  • φ_{m} = (vec(A_{m,1}),...,vec(A_{m,p})

  • and σ_{m} = vech(Ω_{m}), m=1,...,M,

  • ν=(ν_{M1+1},...,ν_{M})

  • M1 is the number of GMVAR type regimes.

For constrained models:

Should be size ((M(d+d(d+1)/2+2)+q-M1-1)x1) and have the form θ = (φ_{1,0},...,φ_{M,0},ψ, σ_{1},...,σ_{M},α_{1},...,α_{M-1},ν), where

  • ψ (qx1) satisfies (φ_{1},..., φ_{M}) = C ψ where C is a (Mpd^2xq) constraint matrix.

For same_means models:

Should have the form θ = (μ,ψ, σ_{1},...,σ_{M},α_{1},...,α_{M-1},ν), where

  • μ= (μ_{1},...,μ_{g}) where μ_{i} is the mean parameter for group i and g is the number of groups.

  • If AR constraints are employed, ψ is as for constrained models, and if AR constraints are not employed, ψ = (φ_{1},...,φ_{M}).

For structural models:

Should have the form θ = (φ_{1,0},...,φ_{M,0},φ_{1},...,φ_{M}, vec(W),λ_{2},...,λ_{M},α_{1},...,α_{M-1},ν), where

  • λ_{m}=(λ_{m1},...,λ_{md}) contains the eigenvalues of the mth mixture component.

If AR parameters are constrained:

Replace φ_{1},..., φ_{M} with ψ (qx1) that satisfies (φ_{1},..., φ_{M}) = C ψ, as above.

If same_means:

Replace (φ_{1,0},...,φ_{M,0}) with (μ_{1},...,μ_{g}), as above.

If W is constrained:

Remove the zeros from vec(W) and make sure the other entries satisfy the sign constraints.

If λ_{mi} are constrained:

Replace λ_{2},...,λ_{M} with γ (rx1) that satisfies (λ_{2},..., λ_{M}) = C_{λ} γ where C_{λ} is a (d(M-1) x r) constraint matrix.

Above, φ_{m,0} is the intercept parameter, A_{m,i} denotes the ith coefficient matrix of the mth mixture component, Ω_{m} denotes the error term covariance matrix of the m:th mixture component, and α_{m} is the mixing weight parameter. The W and λ_{mi} are structural parameters replacing the error term covariance matrices (see Virolainen, 2020). If M=1, α_{m} and λ_{mi} are dropped. If parametrization=="mean", just replace each φ_{m,0} with regimewise mean μ_{m}. vec() is vectorization operator that stacks columns of a given matrix into a vector. vech() stacks columns of a given matrix from the principal diagonal downwards (including elements on the diagonal) into a vector.

In the GMVAR model, M1=M and ν is dropped from the parameter vector. In the StMVAR model, M1=0. In the G-StMVAR model, the first M1 regimes are GMVAR type and the rest M2 regimes are StMVAR type. In StMVAR and G-StMVAR models, the degrees of freedom parameters in ν should be strictly larger than two.

The notation is similar to the cited literature.

model

is "GMVAR", "StMVAR", or "G-StMVAR" model considered? In the G-StMVAR model, the first M1 components are GMVAR type and the rest M2 components are StMVAR type.

m

which component?

regime_pars
For reduced form models:

a size ((pd^2+d+d(d+1)/2)x1) vector (υ_{m},ν_m) = (φ_{m,0},φ_{m},σ_{m},ν_m).

For structural models:

a length pd^2 + d vector (φ_{m,0},φ_{m},ν_m).

In the case of a GMVAR type regime, ν_m is omitted.

structural_pars

If NULL a reduced form model is considered. For structural model, should be a list containing the following elements:

  • W - a (dxd) matrix with its entries imposing constraints on W: NA indicating that the element is unconstrained, a positive value indicating strict positive sign constraint, a negative value indicating strict negative sign constraint, and zero indicating that the element is constrained to zero.

  • C_lambda - a (d(M-1) x r) constraint matrix that satisfies (λ_{2},..., λ_{M}) = C_{λ} γ where γ is the new (r x 1) parameter subject to which the model is estimated (similarly to AR parameter constraints). The entries of C_lambda must be either positive or zero. Ignore (or set to NULL) if the eigenvalues λ_{mi} should not be constrained.

See Virolainen (2020) for the conditions required to identify the shocks and for the B-matrix as well (it is W times a time-varying diagonal matrix with positive diagonal entries).

Details

Does not currently support models with AR, mean, or lambda parameter constraints.

Value

Returns parameter vector with m:th regime changed to regime_pars.

Warning

No argument checks!

References

@keywords internal


saviviro/gmvarkit documentation built on Oct. 25, 2021, 2:14 a.m.