swap_parametrization function

Swap the parametrization of a STVAR model

swap_parametrization swaps the parametrization of a STVAR model to "mean" if the current parametrization is "intercept", and vice versa.

swap_parametrization(stvar, calc_std_errors = FALSE)

Arguments

• stvar: object of class "stvar"
• calc_std_errors: should approximate standard errors be calculated?

Returns

Returns an S3 object of class 'stvar' defining a smooth transition VAR model. The returned list contains the following components (some of which may be NULL depending on the use case): - data: The input time series data.

• model: A list describing the model structure.

• params: The parameters of the model.

• std_errors: Approximate standard errors of the parameters, if calculated.

• transition_weights: The transition weights of the model.

• regime_cmeans: Conditional means of the regimes, if data is provided.

• total_cmeans: Total conditional means of the model, if data is provided.

• total_ccovs: Total conditional covariances of the model, if data is provided.

• uncond_moments: A list of unconditional moments including regime autocovariances, variances, and means.

• residuals_raw: Raw residuals, if data is provided.

• residuals_std: Standardized residuals, if data is provided.

• structural_shocks: Recovered structural shocks, if applicable.

• loglik: Log-likelihood of the model, if data is provided.

• IC: The values of the information criteria (AIC, HQIC, BIC) for the model, if data is provided.

• all_estimates: The parameter estimates from all estimation rounds, if applicable.

• all_logliks: The log-likelihood of the estimates from all estimation rounds, if applicable.

• which_converged: Indicators of which estimation rounds converged, if applicable.

• which_round: Indicators of which round of optimization each estimate belongs to, if applicable.

• seeds: The seeds used in the estimation in fitSTVAR, if applicable.

• LS_estimates: The least squares estimates of the parameters in the form $(\phi_{1,0},...,\phi_{M,0},\varphi_1,...,\varphi_M,\alpha$ (intercepts replaced by unconditional means if mean parametrization is used), if applicable.

Details

swap_parametrization is a convenient tool if you have estimated the model in "intercept" parametrization but wish to work with "mean" parametrization in the future, or vice versa.

Examples

## Create a Gaussian STVAR p=1, M=2 model with the weighted relative stationary densities
# of the regimes as the transition weight function; use the intercept parametrization:
theta_122relg <- c(0.734054, 0.225598, 0.705744, 0.187897, 0.259626, -0.000863,
  -0.3124, 0.505251, 0.298483, 0.030096, -0.176925, 0.838898, 0.310863, 0.007512,
  0.018244, 0.949533, -0.016941, 0.121403, 0.573269)
mod122 <- STVAR(p=1, M=2, d=2, params=theta_122relg, parametrization="intercept")
mod122$params[1:4] # The intercept parameters

# Swap from the intercept parametrization to mean parametrization:
mod122mu <- swap_parametrization(mod122)
mod122mu$params[1:4] # The mean parameters

# Swap back to the intercept parametrization:
mod122int <- swap_parametrization(mod122mu)
mod122int$params[1:4] # The intercept parameters

## Create a linear VAR(p=1) model with the intercept parametrization, include
# the two-variate data gdpdef to the model and calculate approximate standard errors:
theta_112 <- c(0.649526, 0.066507, 0.288526, 0.021767, -0.144024, 0.897103,
  0.601786, -0.002945, 0.067224)
mod112 <- STVAR(data=gdpdef, p=1, M=1, params=theta_112, parametrization="intercept",
  calc_std_errors=TRUE)
print(mod112, standard_error_print=TRUE) # Standard errors are printed for the intercepts

# To obtain standard errors for the unconditional means instead of the intercepts,
# swap to mean parametrization:
mod112mu <- swap_parametrization(mod112, calc_std_errors=TRUE)
print(mod112mu, standard_error_print=TRUE) # Standard errors are printed for the means

References

• Anderson H., Vahid F. 1998. Testing multiple equation systems for common nonlinear components. Journal of Econometrics, 84 :1, 1-36.
• Hubrich K., Teräsvirta. T. 2013. Thresholds and Smooth Transitions in Vector Autoregressive Models. CREATES Research Paper 2013-18, Aarhus University.
• Lanne M., Virolainen S. 2025. A Gaussian smooth transition vector autoregressive model: An application to the macroeconomic effects of severe weather shocks. Unpublished working paper, available as arXiv:2403.14216.
• Kheifets I.L., Saikkonen P.J. 2020. Stationarity and ergodicity of Vector STAR models. Econometric Reviews, 39 :4, 407-414.
• Lütkepohl H., Netšunajev A. 2017. Structural vector autoregressions with smooth transition in variances. Journal of Economic Dynamics & Control, 84 , 43-57.
• Tsay R. 1998. Testing and Modeling Multivariate Threshold Models. Journal of the American Statistical Association, 93 :443, 1188-1202.
• Virolainen S. 2025. Identification by non-Gaussianity in structural threshold and smooth transition vector autoregressive models. Unpublished working paper, available as arXiv:2404.19707.