View source: R/GSMVARconstruction.R
gsmvar_to_sgsmvar constructs SGMVAR, SStMVAR, or SG-StMVAR model based on a reduced
form GMVAR, StMVAR, or G-StMVAR model.
gsmvar_to_sgsmvar(gsmvar, calc_std_errors = TRUE, cholesky = FALSE)
an object of class
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.
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
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.
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
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. 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 Unpublished working paper, available as arXiv:2007.04713.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 Unpublished working paper, available as arXiv:2109.13648.
# 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
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