update_numtols {gmvarkit}

Update the stationarity and positive definiteness numerical tolerances of an existing class 'gsmvar' model.

Description

update_numtols updates the stationarity and positive definiteness numerical tolerances of an existing class 'gsmvar' model.

Usage

update_numtols(gsmvar, stat_tol = 0.001, posdef_tol = 1e-08, df_tol = 1e-08)

Arguments

gsmvar

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

stat_tol

numerical tolerance for stationarity of the AR parameters: if the "bold A" matrix of any regime has eigenvalues larger that 1 - stat_tol the model is classified as non-stationary. Note that if the tolerance is too small, numerical evaluation of the log-likelihood might fail and cause error.

posdef_tol

numerical tolerance for positive definiteness of the error term covariance matrices: if the error term covariance matrix of any regime has eigenvalues smaller than this, the model is classified as not satisfying positive definiteness assumption. Note that if the tolerance is too small, numerical evaluation of the log-likelihood might fail and cause error.

df_tol

the parameter vector is considered to be outside the parameter space if all degrees of freedom parameters are not larger than 2 + df_tol.

Details

All signs in any column of W can be swapped without changing the implied reduced form model. Consequently, also the signs in the columns of the B-matrix are swapped. Note that the sign constraints imposed on W (or the B-matrix) are also swapped in the corresponding columns accordingly.

Also the order of the columns of W can be changed (without changing the implied reduced form model) as long as the order of lambda parameters is also changed accordingly. This can be done with the function reorder_W_columns.

Value

Returns an object of class 'gsmvar' defining a structural GSMVAR model with the modified structural parameters and constraints.

References

• 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 Unpublished working paper, available as arXiv:2109.13648.

@keywords internal

See Also

fitGSMVAR, GSMVAR, GIRF, reorder_W_columns, gsmvar_to_sgsmvar, stmvar_to_gstmvar

Examples

# Structural GMVAR(2, 2), d=2 model identified with sign-constraints:
params22s <- c(0.36, 0.121, 0.484, 0.072, 0.223, 0.059, -0.151, 0.395,
  0.406, -0.005, 0.083, 0.299, 0.218, 0.02, -0.119, 0.722, 0.093, 0.032,
  0.044, 0.191, 0.057, 0.172, -0.46, 0.016, 3.518, 5.154, 0.58)
W_22 <- matrix(c(1, 1, -1, 1), nrow=2, byrow=FALSE)
mod22s <- GSMVAR(p=2, M=2, d=2, params=params22s, structural_pars=list(W=W_22))
mod22s

# Update numerical tolerances:
mod22s <- update_numtols(mod22s, stat_tol=1e-4, posdef_tol=1e-9, df_tol=1e-10)
mod22s # The same model