sort_W_and_lambdas: Sort the columns of W matrix by sorting the lambda parameters...

In gmvarkit: Estimate Gaussian and Student's t Mixture Vector Autoregressive Models

Sort the columns of W matrix by sorting the lambda parameters of the second regime to increasing order

Description

sort_W_and_lambdas sorts the columns of W matrix by sorting the lambda parameters of the second regime to increasing order.

Usage

sort_W_and_lambdas(p, M, d, params, model = c("GMVAR", "StMVAR", "G-StMVAR"))

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	the number of time series in the system.
params	a real valued vector specifying the parameter values. For reduced form models: Should be size ((M(pd^2+d+d(d+1)/2+2)-M1-1)x1) and have the form \theta = (\upsilon_{1}, ...,\upsilon_{M}, \alpha_{1},...,\alpha_{M-1},\nu), where \upsilon_{m} = (\phi_{m,0},\phi_{m},\sigma_{m}) \phi_{m} = (vec(A_{m,1}),...,vec(A_{m,p}) and \sigma_{m} = vech(\Omega_{m}), m=1,...,M, \nu=(\nu_{M1+1},...,\nu_{M}) M1 is the number of GMVAR type regimes. For structural model: Should have the form \theta = (\phi_{1,0},...,\phi_{M,0},\phi_{1},...,\phi_{M}, vec(W),\lambda_{2},...,\lambda_{M},\alpha_{1},...,\alpha_{M-1},\nu), where \lambda_{m}=(\lambda_{m1},...,\lambda_{md}) contains the eigenvalues of the mth mixture component. Above, \phi_{m,0} is the intercept parameter, A_{m,i} denotes the ith coefficient matrix of the mth mixture component, \Omega_{m} denotes the error term covariance matrix of the m:th mixture component, and \alpha_{m} is the mixing weight parameter. The W and \lambda_{mi} are structural parameters replacing the error term covariance matrices (see Virolainen, 2022). If M=1, \alpha_{m} and \lambda_{mi} are dropped. If parametrization=="mean", just replace each \phi_{m,0} with regimewise mean \mu_{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 \nu 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 \nu # should be strictly larger than two. The notation is similar to the cited literature.

Details

Only structural models are supported (but there is no need to provide structural_pars). This function does not sort the constraints of the W matrix but just sorts the columns of the W matrix and the lambda parameters. It is mainly used in the genetic algorithm to assist estimation with better identification when the constraints are not itself strong for identification of the parameters (but are invariant to different orderings of the columns of the W matrix).

Before using this function, make sure the parameter vector is sortable: the constraints on the W matrix is invariant to different orderings of the columns, there are no zero restrictions, and there are no constraints on the lambda parameters.

Value

Returns the sorted parameter vector (that implies the same reduced form model).

Warning

No argument checks!

References

• Virolainen S. 2022. Structural Gaussian mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks. Unpublished working paper, available as arXiv:2007.04713.

• Virolainen S. 2022. Gaussian and Student's t mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks in the Euro area. Unpublished working paper, available as arXiv:2109.13648.

gmvarkit documentation built on Nov. 15, 2023, 1:07 a.m.