# gmvarkit

The goal of gmvarkit is to provide tools to analyse the Gaussian mixture vector autoregressive (GMVAR) model. `gmvarkit`

provides functions for unconstrained and constrained maximum likelihood estimation of the model parameters, quantile residual based model diagnostics, simulation from the processes, and forecasting.

## Installation

You can install the released version of gmvarkit from CRAN with:

And the development version from GitHub with:

## Example

## Simple example

This is a basic example how to estimate a GMVAR model to data. The example data is the same that is used by Kalliovirta et al. (2016) in their paper introducing the GMVAR model. The estimation process is computationally demanding and takes advantage of parallel computing. After estimating the model, it’s shown by simple examples how to conduct some further analysis.

```
# These examples use the data 'eurusd' which comes with the package, but in a scaled form.
data(eurusd, package="gmvarkit")
data <- cbind(10*eurusd[,1], 100*eurusd[,2])
colnames(data) <- colnames(eurusd)
# Estimate a GMVAR(2,2) model
fit <- fitGMVAR(data, p=2, M=2)
fit
# Estimate a 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))
fitc <- fitGMVAR(data, p=2, M=2, constraints=C_mat)
fitc
# Further information on the estimated model:
plot(fitc)
summary(fitc)
print_std_errors(fitc)
get_gradient(fitc) # The first order condition
get_soc(fitc) # The second order condition (eigenvalues of approximated Hessian)
# Quantile residual diagnostics
diagnostic_plot(fitc, type="series") # type=c("series", "ac", "ch", "norm")
qrt <- quantile_residual_tests(fitc)
# Simulate a sample path form the estimated process
sim <- simulateGMVAR(fitc, nsimu=10)
# Forecast future values of the process
predict(fitc, n_ahead=10)
```

## 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*Unpublished Revision of HECER Discussion Paper No. 247*.