gmvar_to_sgmvar {gmvarkit}

DEPRECATED! USE THE FUNCTION fitGSMVAR INSTEAD! Switch from two-regime reduced form GMVAR model to a structural model.

Description

DEPRECATED! USE THE FUNCTION fitGSMVAR INSTEAD! gsmvar_to_sgsmvar constructs SGMVAR model based on a reduced form GMVAR, StMVAR, or G-StMVAR model.

Usage

gmvar_to_sgmvar(gmvar, calc_std_errors = TRUE)

Arguments

gmvar

object of class 'gmvar'

calc_std_errors

should approximate standard errors be calculated?

Details

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.

Value

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.

References

• 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. (forthcoming). A statistically identified structural vector autoregression with endogenously switching volatility regime. Journal of Business & Economic Statistics.

• 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.

See Also

gsmvar_to_sgsmvar