View source: R/GSMVARconstruction.R

gsmvar_to_sgsmvar | R Documentation |

`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)
```

`gsmvar` |
an object of class |

`calc_std_errors` |
should approximate standard errors be calculated? |

`cholesky` |
if |

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
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.

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.

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 Unpublished working paper, available as arXiv:2007.04713.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 Unpublished working paper, available as arXiv:2109.13648.

`fitGSMVAR`

, `GSMVAR`

, `GIRF`

, `reorder_W_columns`

,
`swap_W_signs`

, `stmvar_to_gstmvar`

```
# 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
```

saviviro/gmvarkit documentation built on April 18, 2023, 8:55 a.m.

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