gmvarkit (version 2.1.4)

gsmvar_to_sgsmvar: Switch from two-regime reduced form GMVAR, StMVAR, or G-StMVAR model to a structural model.

Description

gsmvar_to_sgsmvar constructs SGMVAR, SStMVAR, or SG-StMVAR model based on a reduced form GMVAR, StMVAR, or G-StMVAR model.

Usage

gsmvar_to_sgsmvar(gsmvar, calc_std_errors = TRUE, cholesky = FALSE)

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.

Arguments

gsmvar

an object of class 'gsmvar', typically created with fitGSMVAR or GSMVAR.

calc_std_errors

should approximate standard errors be calculated?

cholesky

if M == 1, should the lower triangular Cholesky identification be employed? See details for using Cholesky identification with M > 1.

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.

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. 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.

See Also

fitGSMVAR, GSMVAR, GIRF, reorder_W_columns, swap_W_signs, stmvar_to_gstmvar

Examples

# \donttest{
# Reduced form GMVAR(1,2) model
params12 <- c(0.55, 0.112, 0.344, 0.055, -0.009, 0.718, 0.319,
 0.005, 0.03, 0.619, 0.173, 0.255, 0.017, -0.136, 0.858, 1.185,
 -0.012, 0.136, 0.674)
mod12 <- GSMVAR(gdpdef, p=1, M=2, params=params12)

# Form a structural model based on the reduced form model:
mod12s <- gsmvar_to_sgsmvar(mod12)
mod12s

#' # Reduced form StMVAR(1,2) model
mod12t <- GSMVAR(gdpdef, p=1, M=2, params=c(params12, 11, 12), model="StMVAR")

# Form a structural model based on the reduced form model:
mod12ts <- gsmvar_to_sgsmvar(mod12t)
mod12ts
# }