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gmvarkit

The goal of gmvarkit is to provide tools to work with Gaussian Mixture Vector Autoregressive (GMVAR) model. Most importantly gmvarkit provides function fitGMVAR for two phase maximum likelihood estimation, but it also constains functions for quantile residual tests, graphical diagostics, forecasting and simulations. Also applying general linear constraints to the autoregressive parameters is supported.

Simple example

This is a basic example how to estimate a GMVAR model to an example data. The estimation process is computationally heavy and uses parallel computing.

# These examples use the data 'eurusd' which comes with the package, but in a scaled form.
data <- cbind(10*eurusd[,1], 100*eurusd[,2])
colnames(data) <- colnames(eurusd)

# GMVAR(2,2) model
fit22 <- fitGMVAR(data, p=2, M=2)
fit22

# GMVAR(2,2) model with autoregressive parameters restricted to be the same for all regimes
C_mat <- rbind(diag(2*2^2), diag(2*2^2))
fit22c <- fitGMVAR(data, p=2, M=2, constraints=C_mat)
fit22c

References

Kalliovirta L., Meitz M. and Saikkonen P. (2016) Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
Kalliovirta L. and Saikkonen P. (2010) Reliable Residuals for Multivariate Nonlinear Time Series Models. Unpublished Revision of HECER Discussion Paper No. 247.

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Version

Install

install.packages('gmvarkit')

Monthly Downloads

538

Version

1.0.1

License

GPL-3

Maintainer

Savi Virolainen

Last Published

August 13th, 2018

Functions in gmvarkit (1.0.1)

Check the stationary condition of given GMVAR model

Pick coefficient all matrices

pick_all_phi0_A

Pick all \(\phi_{m,0}\) or \(\mu_{m}\) and \(A_{m}\) parameter values from the given parameter vector.

random_coefmats2

Create somewhat random stationary VAR model \((dxd)\) coefficient matrices \(A\).

Create somewhat random VAR model error term covariance matrix

Create somewhat random mean-parametrized parameter vector of GMVAR model, that may not be stationary!

check_constraints

Check the constraint matrix has the correct form

Check the data is in the correct form

change_parametrization

Change parametrization of the parameter vector

Change regime parameters \(\upsilon_{m}\)\( = (\phi_{m,0},\)\(\phi_{m}\)\(,\sigma_{m})\) of the given parameter vector.

Check that p, M and d are correctly set

Create somewhat random parameter vector of GMVAR model that is always stationary

check_parameters

Check that the given parameter vector satisfies model assumptions

Check whether all arguments are positive scalar whole numbers

Compute log-likelihood of GMVAR model using parameter vector

loglikelihood_int

Compute the log-likelihood of Gaussian Mixture Vector Autoregressive model

Form the \(((dp)x(dp))\) "bold A" matrices related to the VAR processes

Calculate gradient or Hessian matrix

Calculate the number of parameters in GMVAR model parameter vector

Pick coefficient matrices

Function factory for value formatting

diagnostic_plot

Quantile residual diagnostic plot for GMVAR model

gmvarkit: Estimate Gaussian Mixture Vector Autoregressive (GMVAR) model

Add data to object of class 'gmvar' defining a GMVAR model

Calculate logarithms of multiple multivariate normal densities with varying mean and constant covariance matrix

Predict method for class 'gmvar' objects

Calculate AIC, HQIC and BIC

Genetic algorithm for preliminary estimation of GMVAR model

Create object of class 'gmvar' defining a GMVAR model

Euro area and U.S. long-term government bond yields and Euro-U.S. dollar exchange rate.

Determine whether the parameter vector lies in the parameter space or not

in_paramspace_int

Determine whether the parameter vector lies in the parameter space or not

Quantile residual tests

print.gmvarpred

print method for class 'gmvarpred' objects

Checks whether the given object has class attribute "gmvar"

regime_distance

Calculate "distance" between two (scaled) regimes \(\upsilon_{m}\)\( = (\phi_{m,0},\)\(\phi_{m}\)\(,\sigma_{m})\)

check_null_data

Checks whether the given object contains data or not

Pick mixing weight parameters \(\alpha_{m}, m=1,...,M\) from the given parameter vector.

Simulate from GMVAR process

get_regime_means

Calculate and return regime means \(\mu_{m}\)

quantile_residuals

Calculate multivariate quantile residuals of GMVAR model

sort_components

Sort components in parameter vector by mixing weights into a decreasing order

standard_errors

Calculate standard errors for estimates of GMVAR model

Parsimonious vectorization operator for symmetric matrices.

get_regime_means_int

Calculate and return regime means \(\mu_{m}\)

Two-phase maximum likelihood estimation of GMVAR model

Compute covariance matrix Omega used in quantile residual tests

Pick regime parameters \(\upsilon_{m}\)\( = (\phi_{m,0},\)\(\phi_{m}\)\(,\sigma_{m})\) from the given parameter vector.

Pick coefficient matrix

Pick covariance matrices

Pick \(\phi_{m,0}\) or \(\mu_{m}\), m=1,..,M vectors from the given parameter vector

plot method for class 'gmvarpred' objects

reform_constrained_pars

Reform constrained parameter vector into the "standard" form

quantile_residuals_int

Calculate multivariate quantile residuals of GMVAR model

print_std_errors

Print standard errors of GMVAR model in the same form as the model estimates are printed

Summary print method from objects of class 'gmvarsum'

swap_parametrization

Swap the parametrization of object of class 'gmvar' defining a GMVAR model

random_coefmats

Create random VAR-model \((dxd)\) coefficient matrices \(A\).

Reverse operator of the parsimonious vectorization operator vech().

Create somewhat random VAR-model \((dxd)\) error term covariance matrix \(\Omega\) fairly close to a given positive definite covariance matrix using (scaled) Wishart distribution.

Create somewhat random parameter vector of GMVAR model fairly close to a given parameter vector

Reverse vectorization operator.

Vectorization operator.

Maximum likelihood estimation of GMVAR model with preliminary estimates