DEPRECATED! USE THE FUNCTION fitGSMVAR INSTEAD!
gsmvar_to_sgsmvar constructs SGMVAR model based on a reduced
form GMVAR, StMVAR, or G-StMVAR model.
gmvar_to_sgmvar(gmvar, calc_std_errors = TRUE)Returns an object of class 'gsmvar' defining a structural GMVAR, StMVAR, or G-StMVAR model based on a
two-regime reduced form GMVAR, StMVAR, or G-StMVAR model, with the main diagonal of the B-matrix normalized to be
positive.
object of class 'gmvar'
should approximate standard errors be calculated?
The switch is made by simultaneously diagonalizing the two error term covariance matrices
with a well known matrix decomposition (Muirhead, 1982, Theorem A9.9) and then normalizing the
diagonal of the matrix W positive (which implies positive diagonal of the B-matrix). Models with
more that two regimes are not supported because the matrix decomposition does not generally
exists for more than two covariance matrices. If the model has only one regime (= regular SVAR model),
a symmetric and pos. def. square root matrix of the error term covariance matrix is used unless
cholesky = TRUE is set in the arguments, in which case Cholesky identification is employed.
In order to employ a structural model with Cholesky identification and multiple regimes (M > 1),
use the function GIRF directly with a reduced form model (see ?GIRF).
The columns of \(W\) as well as the lambda parameters can be re-ordered (without changing the implied
reduced form model) afterwards with the function reorder_W_columns. Also all signs in any column
of \(W\) can be swapped (without changing the implied reduced form model) afterwards with the function
swap_W_signs. These two functions work with models containing any number of regimes.
Muirhead R.J. 1982. Aspects of Multivariate Statistical Theory, Wiley.
Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
Virolainen S. 2025. A statistically identified structural vector autoregression with endogenously switching volatility regime. Journal of Business & Economic Statistics, 43, 1, 44-54.
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 Unpublished working paper, available as arXiv:2109.13648.
gsmvar_to_sgsmvar