alt_stvar function

Construct a STVAR model based on results from an arbitrary estimation round of fitSTVAR

alt_stvar constructs a STVAR model based on results from an arbitrary estimation round of fitSTVAR

alt_stvar(stvar, which_largest = 1, which_round, calc_std_errors = FALSE)

Arguments

• stvar: object of class "stvar"
• which_largest: based on estimation round with which largest log-likelihood should the model be constructed? An integer value in 1,...,nrounds. For example, which_largest=2 would take the second largest log-likelihood and construct the model based on the corresponding estimates.
• which_round: based on which estimation round should the model be constructed? An integer value in 1,...,nrounds. If specified, then which_largest is ignored.
• 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

It's sometimes useful to examine other estimates than the one with the highest log-likelihood. This function is wrapper around STVAR that picks the correct estimates from an object returned by fitSTVAR.

Examples

## These are long-running examples that take approximately 10 seconds to run.

# Estimate a Gaussian STVAR p=1, M=2 model with threshold weight function and
# the first lag of the second variable as the switching variables. Run only two
# estimation rounds and use the two-phase estimation method:
fit12 <- fitSTVAR(gdpdef, p=1, M=2, weight_function="threshold", weightfun_pars=c(2, 1),
 nrounds=2, seeds=c(1, 4), estim_method="two-phase")
fit12$loglik # Log-likelihood of the estimated model

# Print the log-likelihood obtained from each estimation round:
fit12$all_logliks

# Construct the model based on the second largest log-likelihood found in the
# estimation procedure:
fit12_alt <- alt_stvar(fit12, which_largest=2, calc_std_errors=FALSE)
fit12_alt$loglik # Log-likelihood of the alternative solution

# Construct a model based on a specific estimation round, the first round:
fit12_alt2 <- alt_stvar(fit12, which_round=1, calc_std_errors=FALSE)
fit12_alt2$loglik # Log-likelihood of the alternative solution

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.

See Also

STVAR