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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

579

Version

3.2.1

License

GPL-3

Maintainer

Savi Virolainen

Last Published

December 11th, 2019

Functions in uGMAR (3.2.1)

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

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

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

Check that the argument model is correctly specified.

check_params_length

Check that the parameter vector has the correct dimension

change_parametrization

Change parametrization of the parameter vector

checkAndCorrectData

Check the data is set correctly and correct if not

Extract regime from a parameter vector

Estimate Gaussian or Student's t Mixture Autoregressive model

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

get_regime_vars

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

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

Generate covariance matrix Omega for quantile residual tests

Check p and M are correctly set

Calculate the number of parameters

checkConstraintMat

Check the constraint matrices

Function factory for value formatting

parameterChecks

Check the parameter vector is specified correctly

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

Check that given object contains data

get_regime_autocovs

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

Check that given object has class attribute 'gsmar'

get_regime_means

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

plot method for class 'gsmarpred' objects

Forecast GMAR, StMAR or G-StMAR process

isStationary_int

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

Pick degrees of freedom parameters from parameter vector

Pick mixing weights parameters from parameter vector

quantileResidualPlot

Ploy quantile residual time series and kernel density

loglikelihood_int

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

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

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

quantileResiduals

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

quantileResiduals_int

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

stmarpars_to_gstmar

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

randomIndividual

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

randomIndividual_int

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

stmar_to_gstmar

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

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

Warn about large degrees of freedom parameter values

regime_distance

Calculate "distance" between two regimes

reformRestrictedPars

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

removeAllConstraints

Transform constrained and restricted parameter vector into the regular form

Simulate values from GMAR, StMAR or G-StMAR process

mixingWeights_int

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

print.gsmarpred

print method for class 'gsmarpred' objects

Create random regime

Print method from objects of class 'gsmarsum'

Create random AR coefficients

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

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

uncondMoments_int

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

Calculate AIC, HQIC and BIC

Calculate absolute values of the roots of the AR characteristic polynomials

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

CBOE Volatility Index: logVIX

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

Pick phi0 or mean parameters from parameter vector

reformConstrainedPars

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

reformParameters

Reform any parameter vector into standard form.

swap_parametrization

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

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

Calculate gradient or Hessian matrix

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

University of Michigan: inflation expectation time series: IE

CBOE Volatility Index: VIX

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

Check whether all arguments are positive scalar whole numbers

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

Add random dfs to a vector