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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)
profile_logliks(fit) # Plot the profile log-likelihood functions

## 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, pi=c(0.95, 0.8))

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 **
Virolainen S. 2020. A mixture autoregressive model based on Gaussian and Student’s t-distribution. arXiv:2003.05221 [econ.EM].

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Version

Install

install.packages('uGMAR')

Monthly Downloads

392

Version

3.2.4

License

GPL-3

Maintainer

Savi Virolainen

Last Published

March 20th, 2020

Functions in uGMAR (3.2.4)

Add random dfs to a vector

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

Check whether all arguments are stricly positive natural numbers

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

Check that p and M are correctly set

checkConstraintMat

Check the constraint matrices

Calculate gradient or Hessian matrix

Function factory for formatting values

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

Check that given object contains data

Check that given object has class attribute 'gsmar'

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

Extract regime from a parameter vector

Estimate Gaussian or Student's t Mixture Autoregressive model

change_parametrization

Change parametrization of a parameter vector

Generate the covariance matrix Omega for quantile residual tests

Calculate AIC, HQIC and BIC

loglikelihood_int

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

Calculate absolute values of the roots of the AR characteristic polynomials

print.gsmarpred

Print method for class 'gsmarpred' objects

Forecast GMAR, StMAR, or G-StMAR process

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

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

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

mixingWeights_int

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

Pick phi0 or mean parameters from parameter vector

Plot method for class 'gsmarpred' objects

Quantile residual tests for GMAR, StMAR , and G-StMAR models

quantileResidualPlot

Plot quantile residual time series and histogram

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

removeAllConstraints

Transform constrained and restricted parameter vector into the regular form

Simulate values from GMAR, StMAR, and G-StMAR processes

randomIndividual

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

Calculate the number of parameters

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

randomIndividual_int

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

parameterChecks

Check the parameter vector is specified correctly

Pick mixing weights parameters from parameter vector

checkAndCorrectData

Check that the data is set correctly and correct if not

Spread between 10-Year and 1-Year treasury rates: T10Y1Y

Check that the argument 'model' is correctly specified.

check_params_length

Check that the parameter vector has the correct dimension

CBOE Volatility Index: VIX

get_regime_means

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

reformConstrainedPars

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

get_regime_vars

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

Returns the default smallest allowed log-likelihood for given data.

get_regime_autocovs

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

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

reformParameters

Reform any parameter vector into standard form.

reformRestrictedPars

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

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

uncondMoments_int

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

CBOE Volatility Index: logVIX

regime_distance

Calculate "distance" between two regimes

Print method from objects of class 'gsmarsum'

isStationary_int

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

Pick degrees of freedom parameters from a parameter vector

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

Create random AR coefficients

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

profile_logliks

Plot profile log-likehoods around the estimates

uGMAR: Estimate Univariate Gaussian and Student's t Mixture Autoregressive Models

Warn about large degrees of freedom parameter values

Create random regime parameters

swap_parametrization

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

stmar_to_gstmar

Estimate a G-StMAR model based on a 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.

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

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

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