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uGMAR

The goal of uGMAR is to provide tools for analysing Gaussian mixture autoregressive (GMAR), Student’s t mixture Autoregressive (StMAR) and Gaussian and Student’s t mixture autoregressive (G-StMAR) models. uGMAR 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 uGMAR from CRAN with:

install.packages("uGMAR")

And the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("saviviro/uGMAR")

Example

This is a basic example how to estimate a GMAR model to data. For details about the example data “logVIX” see ?logVIX. 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.

## Estimate a GMAR(1, 2) model to logarithmized VIX data
data(logVIX, package="uGMAR")
fit <- fitGSMAR(data=logVIX, p=1, M=2, model="GMAR")
fit
summary(fit) # Approximate standard errors in brackets
plot(fit)

get_gradient(fit) # The first order condition
get_soc(fit) # The second order condition (eigenvalues of approximated Hessian)

## Quantile residual diagnostics
quantileResidualPlot(fit)
diagnosticPlot(fit)
qrt <- quantileResidualTests(fit)

## Simulate a sample path from the estimated process
sim <- simulateGSMAR(fit, nsimu=10)

## Forecast future values of the process
predict(fit, n_ahead=10)

References

Kalliovirta L., Meitz M. and Saikkonen P. 2015. Gaussian Mixture Autoregressive model for univariate time series. Journal of Time Series Analysis, 36, 247-266.
Meitz M., Preve D., Saikkonen P. 2018. A mixture autoregressive model based on Student’s t-distribution. arXiv:1805.04010 ** eco**n.E**M **
There are currently no published references for the G-StMAR model, but it’s a straightforward generalization with theoretical properties similar to the GMAR and StMAR models.

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Version

Install

install.packages('uGMAR')

Monthly Downloads

392

Version

3.2.0

License

GPL-3

Maintainer

Savi Virolainen

Last Published

August 27th, 2019

Functions in uGMAR (3.2.0)

Add data to object of class 'gsmar' defining a GMAR, StMAR or G-StMAR model

Calculate gradient or Hessian matrix

Check whether all arguments are positive scalar whole numbers

University of Michigan: inflation expectation time series: IE

Add random dfs to a vector

Genetic algorithm for preliminary estimation of GMAR, StMAR or G-StMAR model

Change the specified regime of parameter vector to the given regime-parameter vector

Construct a GSMAR model based on results from an arbitrary estimation round of fitGSMAR

CBOE Volatility Index: VIX

Create object of class 'gsmar' defining a GMAR, StMAR or G-StMAR model

Check that given object contains data

Quantile residual based diagnostic plots for GMAR, StMAR and G-StMAR models

Calculate conditional moments of GMAR, StMAR or G-StMAR model

get_regime_vars

Calculate regime specific variances \(\gamma_{m,0}\)

checkConstraintMat

Check the constraint matrices

Get differences 'h' which are adjusted for overly large degrees of freedom parameters

Check p and M are correctly set

change_parametrization

Change parametrization of the parameter vector

checkAndCorrectData

Check the data is set correctly and correct if not

Check that the argument model is correctly specified.

check_params_length

Check that the parameter vector has the correct dimension

get_regime_autocovs

Calculate regime specific autocovariances \(\gamma\)\(_{m,p}\)

Calculate AIC, HQIC and BIC

Calculate the number of parameters

Compute the log-likelihood of GMAR, StMAR or G-StMAR model

quantileResidualPlot

Ploy quantile residual time series and kernel density

parameterChecks

Check the parameter vector is specified correctly

Check that given object has class attribute 'gsmar'

get_regime_means

Calculate regime specific means \(\mu_{m}\)

Function factory for value formatting

Estimate Gaussian or Student's t Mixture Autoregressive model

Extract regime from a parameter vector

Quantile residual tests for GMAR, StMAR or G-StMAR model

Generate covariance matrix Omega for quantile residual tests

isStationary_int

Check the stationary and identification conditions of specified GMAR, StMAR or G-StMAR model.

Check the stationary condition of specified GMAR, StMAR or G-StMAR model.

Pick \(\phi_0\) (or \(\mu\)), AR-coefficients and variance parameters from parameter vector

Pick phi0 or mean parameters from parameter vector

reformConstrainedPars

Reform parameter vector with linear constraints to correspond non-constrained parameter vector.

Maximum likelihood estimation of GMAR, StMAR or G-StMAR model with preliminary estimates

CBOE Volatility Index: logVIX

print.gsmarpred

print method for class 'gsmarpred' objects

Print method from objects of class 'gsmarsum'

Pick mixing weights parameters from parameter vector

Calculate absolute values of the roots of the AR characteristic polynomials

Pick degrees of freedom parameters from parameter vector

randomIndividual_int

Create random GMAR, StMAR or G-StMAR model compatible parameter vector

randomIndividual

Create random GMAR, StMAR or G-StMAR model compatible parameter vector

reformRestrictedPars

Reform parameter vector with restricted autoregressive parameters to correspond non-restricted parameter vector.

Calculate mixing weights of GMAR, StMAR or G-StMAR model

regime_distance

Calculate "distance" between two regimes

mixingWeights_int

Calculate mixing weights of GMAR, StMAR or G-StMAR model

Create random AR coefficients

plot method for class 'gsmarpred' objects

loglikelihood_int

Compute the log-likelihood of GMAR, StMAR or G-StMAR model

Forecast GMAR, StMAR or G-StMAR process

swap_parametrization

Swap the parametrization of object of class 'gsmar' defining a gsmar model

Calculate unconditional mean, variance, first p autocovariances and autocorrelations of the GSMAR process.

reformParameters

Reform any parameter vector into standard form.

uncondMoments_int

Calculate unconditional mean, variance, first p autocovariances and autocorrelations of the GSMAR process.

Create random regime

uGMAR: Estimate Univariate Gaussian or Student's t Mixture Autoregressive Model

Warn about large degrees of freedom parameter values

stmar_to_gstmar

Estimate a G-StMAR model based on StMAR model with large degrees of freedom parameters

stmarpars_to_gstmar

Transform a StMAR model parameter vector to a corresponding G-StMAR model parameter vector with large dfs parameters reduced.

quantileResiduals

Compute quantile residuals of GMAR, StMAR or G-StMAR model

quantileResiduals_int

Compute quantile residuals of GMAR, StMAR or G-StMAR model

Calculate standard errors for estimates of GMAR, StMAR or GStMAR model

Sort the mixture components of GMAR, StMAR or G-StMAR model

removeAllConstraints

Transform constrained and restricted parameter vector into the regular form

Simulate values from GMAR, StMAR or G-StMAR process