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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

353

Version

3.2.3

License

GPL-3

Maintainer

Savi Virolainen

Last Published

March 12th, 2020

Functions in uGMAR (3.2.3)

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

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

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

Calculate gradient or Hessian matrix

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

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

Check whether all arguments are stricly positive natural numbers

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

Add random dfs to a vector

CBOE Volatility Index: VIX

Check that given object contains data

check_params_length

Check that the parameter vector has the correct dimension

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

Check that the argument 'model' is correctly specified.

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

checkAndCorrectData

Check that the data is set correctly and correct if not

change_parametrization

Change parametrization of a parameter vector

Check that p and M are correctly set

checkConstraintMat

Check the constraint matrices

Check that given object has class attribute 'gsmar'

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

Calculate absolute values of the roots of the AR characteristic polynomials

get_regime_means

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

get_regime_vars

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

Calculate AIC, HQIC and BIC

get_regime_autocovs

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

Extract regime from a parameter vector

Estimate Gaussian or Student's t Mixture Autoregressive model

Generate the covariance matrix Omega for quantile residual tests

Function factory for formatting values

loglikelihood_int

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

CBOE Volatility Index: logVIX

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

isStationary_int

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

Calculate the number of parameters

mixingWeights_int

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

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

Print method from objects of class 'gsmarsum'

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

print.gsmarpred

Print method for class 'gsmarpred' objects

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

profile_logliks

Plot profile log-likehoods around the estimates

Forecast GMAR, StMAR, or G-StMAR process

Pick degrees of freedom parameters from a parameter vector

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

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

quantileResidualPlot

Plot quantile residual time series and histogram

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

Plot method for class 'gsmarpred' objects

Pick phi0 or mean parameters from parameter vector

quantileResiduals

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

quantileResiduals_int

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

Create random regime parameters

Create random AR coefficients

reformConstrainedPars

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

reformParameters

Reform any parameter vector into standard form.

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.

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

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

swap_parametrization

Swap the parametrization of object of class 'gsmar' defining a GMAR, StMAR, or G-StMAR model

parameterChecks

Check the parameter vector is specified correctly

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

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

Pick mixing weights parameters from parameter vector

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

regime_distance

Calculate "distance" between two regimes

Warn about large degrees of freedom parameter values

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

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.