# Estimate Gaussian and Student's t Mixture Vector Autoregressive Models

## Documentation for package ‘gmvarkit’ version 2.1.2

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

gmvarkit-package | gmvarkit: Estimate Gaussian and Student's t Mixture Vector Autoregressive Models
add_data | Add data to an object of class 'gsmvar' defining a GMVAR, StMVAR, or G-StMVAR model
alt_gmvar | DEPRECATED! USE THE FUNCTION alt_gsmvar INSTEAD! Construct a GMVAR model based on results from an arbitrary estimation round of 'fitGSMVAR'
alt_gsmvar | Construct a GMVAR, StMVAR, or G-StMVAR model based on results from an arbitrary estimation round of 'fitGSMVAR'
calc_gradient | Calculate gradient or Hessian matrix
calc_hessian | Calculate gradient or Hessian matrix
check_parameters | Check that the given parameter vector satisfies the model assumptions
cond_moments | Compute conditional moments of a GMVAR, StMVAR, or G-StMVAR model
cond_moment_plot | Conditional mean or variance plot for a GMVAR, StMVAR, or G-StMVAR model
diagnostic_plot | Quantile residual diagnostic plot for a GMVAR, StMVAR, or G-StMVAR model
diag_Omegas | Simultaneously diagonalize two covariance matrices
estimate_sgsmvar | Maximum likelihood estimation of a structural GMVAR, StMVAR, or G-StMVAR model with preliminary estimates

euromone

A monthly Euro area data covering the period from January 1999 to December 2021 (276 observations) and consisting four variables: cyclical component of log industrial production index, the log-difference of harmonized consumer price index, the log-difference of Brent crude oil prices (Europe), and an interest rate variable. The interest rate variable is the Euro overnight index average rate (EONIA) from January 1999 to October 2008, and after that the Wu and Xia (2016) shadow rate, which is not constrained by the zero lower bound and also quantifies unconventional monetary policy measures. The log-difference of the harmonized consumer price index is multiplied by hundred and the log-difference of oil price by ten. This data is the one that was used in Virolainen (2022).

fitGMVAR | DEPRECATED! USE THE FUNCTION fitGSMVAR INSTEAD! Two-phase maximum likelihood estimation of a GMVAR model
fitGSMVAR | Two-phase maximum likelihood estimation of a GMVAR, StMVAR, or G-StMVAR model
GAfit | Genetic algorithm for preliminary estimation of a GMVAR, StMVAR, or G-StMVAR model
gdpdef | U.S. real GDP percent change and GDP implicit price deflator percent change.
get_boldA_eigens | Calculate absolute values of the eigenvalues of the "bold A" matrices containing the AR coefficients
get_foc | Calculate gradient or Hessian matrix
get_gradient | Calculate gradient or Hessian matrix
get_hessian | Calculate gradient or Hessian matrix
get_omega_eigens | Calculate the eigenvalues of the "Omega" error term covariance matrices
get_regime_autocovs | Calculate regimewise autocovariance matrices
get_regime_means | Calculate regime means mu_{m}
get_soc | Calculate gradient or Hessian matrix
GFEVD | Estimate generalized forecast error variance decomposition for structural (and reduced form) GMVAR, StMVAR, and G-StMVAR models.
GIRF | Estimate generalized impulse response function for structural (and reduced form) GMVAR, StMVAR, and G-StMVAR models.
GMVAR | DEPRECATED! USE THE FUNCTION GSMVAR INSTEAD! Create a class 'gsmvar' object defining a reduced form or structural GMVAR model
gmvarkit | gmvarkit: Estimate Gaussian and Student's t Mixture Vector Autoregressive Models
gmvar_to_gsmvar | Makes class 'gmvar' objects compatible with the functions using class 'gsmvar' objects
gmvar_to_sgmvar | DEPRECATED! USE THE FUNCTION fitGSMVAR INSTEAD! Switch from two-regime reduced form GMVAR model to a structural model.
GSMVAR | Create a class 'gsmvar' object defining a reduced form or structural GMVAR, StMVAR, or G-StMVAR model
gsmvar_to_sgsmvar | Switch from two-regime reduced form GMVAR, StMVAR, or G-StMVAR model to a structural model.
in_paramspace | Determine whether the parameter vector lies in the parameter space
in_paramspace_int | Determine whether the parameter vector lies in the parameter space
iterate_more | Maximum likelihood estimation of a GMVAR, StMVAR, or G-StMVAR model with preliminary estimates
linear_IRF | Estimate linear impulse response function based on a single regime of a structural GMVAR, StMVAR, or G-StMVAR model.
logLik.gmvar | Deprecated S3 methods for the deprecated class 'gmvar'
logLik.gsmvar | Create a class 'gsmvar' object defining a reduced form or structural GMVAR, StMVAR, or G-StMVAR model
loglikelihood | Compute log-likelihood of a GMVAR, StMVAR, or G-StMVAR model using parameter vector
LR_test | Perform likelihood ratio test for a GMVAR, StMVAR, or G-StMVAR model
Pearson_residuals | Calculate multivariate Pearson residuals of a GMVAR, StMVAR, or G-StMVAR model
plot.gfevd | Estimate generalized forecast error variance decomposition for structural (and reduced form) GMVAR, StMVAR, and G-StMVAR models.
plot.girf | Estimate generalized impulse response function for structural (and reduced form) GMVAR, StMVAR, and G-StMVAR models.
plot.gmvar | Deprecated S3 methods for the deprecated class 'gmvar'
plot.gmvarpred | plot method for class 'gmvarpred' objects
plot.gsmvar | Create a class 'gsmvar' object defining a reduced form or structural GMVAR, StMVAR, or G-StMVAR model
plot.gsmvarpred | plot method for class 'gsmvarpred' objects
plot.irf | Estimate linear impulse response function based on a single regime of a structural GMVAR, StMVAR, or G-StMVAR model.
plot.qrtest | Quantile residual tests
predict.gmvar | DEPRECATED! USE THE FUNCTION predict.gsmvar INSTEAD! Predict method for class 'gmvar' objects
predict.gsmvar | Predict method for class 'gsmvar' objects
print.gfevd | Estimate generalized forecast error variance decomposition for structural (and reduced form) GMVAR, StMVAR, and G-StMVAR models.
print.girf | Estimate generalized impulse response function for structural (and reduced form) GMVAR, StMVAR, and G-StMVAR models.
print.gmvar | Deprecated S3 methods for the deprecated class 'gmvar'
print.gmvarpred | plot method for class 'gmvarpred' objects
print.gmvarsum | Summary print method from objects of class 'gmvarsum'
print.gsmvar | Create a class 'gsmvar' object defining a reduced form or structural GMVAR, StMVAR, or G-StMVAR model
print.gsmvarpred | Print method for class 'gsmvarpred' objects
print.gsmvarsum | Summary print method from objects of class 'gsmvarsum'
print.hypotest | Print method for the class hypotest
print.irf | Estimate linear impulse response function based on a single regime of a structural GMVAR, StMVAR, or G-StMVAR model.
print.qrtest | Quantile residual tests
print_std_errors | Print standard errors of a GMVAR, StMVAR, or G-StMVAR model in the same form as the model estimates are printed
profile_logliks | Plot profile log-likehoods around the estimates
quantile_residuals | Calculate multivariate quantile residuals of a GMVAR, StMVAR, or G-StMVAR model
quantile_residual_tests | Quantile residual tests
random_ind2 | Create somewhat random parameter vector of a GMVAR, StMVAR, or G-StMVAR model that is always stationary
Rao_test | Perform Rao's score test for a GSMVAR model
redecompose_Omegas | In the decomposition of the covariance matrices (Muirhead, 1982, Theorem A9.9), change the order of the covariance matrices.
reorder_W_columns | Reorder columns of the W-matrix and lambda parameters of a structural GMVAR, StMVAR, or G-StMVAR model.
residuals.gmvar | Deprecated S3 methods for the deprecated class 'gmvar'
residuals.gsmvar | Create a class 'gsmvar' object defining a reduced form or structural GMVAR, StMVAR, or G-StMVAR model
simulate.gsmvar | Simulate method for class 'gsmvar' objects
simulateGMVAR | DEPRECATED! USE THE FUNCTION simulate.gsmvar INSTEAD! Simulate from GMVAR process
stmvar_to_gstmvar | Estimate a G-StMVAR model based on a StMVAR model that has large degrees of freedom parameters
summary.gmvar | Deprecated S3 methods for the deprecated class 'gmvar'
summary.gsmvar | Create a class 'gsmvar' object defining a reduced form or structural GMVAR, StMVAR, or G-StMVAR model
swap_parametrization | Swap the parametrization of a GMVAR, StMVAR, or G-StMVAR model
swap_W_signs | Swap all signs in pointed columns a the W matrix of a structural GMVAR, StMVAR, or G-StMVAR model.
uncond_moments | Calculate the unconditional mean, variance, the first p autocovariances, and the first p autocorrelations of a GMVAR, StMVAR, or G-StMVAR process
update_numtols | Update the stationarity and positive definiteness numerical tolerances of an existing class 'gsmvar' model.

usamon

A quarterly U.S. data covering the period from 1954Q3 to 2021Q4 (270 observations) and consisting four variables: the log-difference of real GDP, the log-difference of GDP implicit price deflator, the log-difference of producer price index (all commodities), and an interest rate variable. The interest rate variable is the effective federal funds rate from 1954Q3 to 2008Q2 and after that the Wu and Xia (2016) shadow rate, which is not constrained by the zero lower bound and also quantifies unconventional monetary policy measures. The log-differences of the GDP, GDP deflator, and producer price index are multiplied by hundred. This data is used in Virolainen (forthcoming).

usamone

A quarterly U.S. data covering the period from 1954Q3 to 2021Q4 (270 observations) and consisting four variables: cyclical component of the log of real GDP, the log-difference of GDP implicit price deflator, the log-difference of producer price index (all commodities), and an interest rate variable. The interest rate variable is the effective federal funds rate from 1954Q3 to 2008Q2 and after that the Wu and Xia (2016) shadow rate, which is not constrained by the zero lower bound and also quantifies unconventional monetary policy measures. The log-differences of the GDP deflator and producer price index are multiplied by hundred.

Wald_test | Perform Wald test for a GMVAR, StMVAR, or G-StMVAR model