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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)

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

3.2.2

License

GPL-3

Maintainer

Savi Virolainen

Last Published

January 16th, 2020

Functions in uGMAR (3.2.2)

Calculate gradient or Hessian matrix

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

Check whether all arguments are stricly positive natural numbers

Check that p and M are correctly set

checkConstraintMat

Check the constraint matrices

Add random dfs to a vector

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

Calculate absolute values of the roots of the AR characteristic polynomials

Calculate AIC, HQIC and BIC

isStationary_int

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

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

Estimate Gaussian or Student's t Mixture Autoregressive model

CBOE Volatility Index: logVIX

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

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

randomIndividual

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

Extract regime from a parameter vector

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

get_regime_means

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

Check that the argument 'model' is correctly specified.

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

get_regime_autocovs

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

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

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

check_params_length

Check that the parameter vector has the correct dimension

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

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

Check that given object contains data

loglikelihood_int

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

Pick phi0 or mean parameters from parameter vector

Create random regime parameters

stmar_to_gstmar

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

Forecast GMAR, StMAR, or G-StMAR process

Create random AR coefficients

Plot method for class 'gsmarpred' objects

Print method from objects of class 'gsmarsum'

print.gsmarpred

Print method for class 'gsmarpred' objects

Pick degrees of freedom parameters from a parameter vector

quantileResidualPlot

Plot quantile residual time series and histogram

Check that given object has class attribute 'gsmar'

get_regime_vars

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

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

stmarpars_to_gstmar

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

parameterChecks

Check the parameter vector is specified correctly

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

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

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

randomIndividual_int

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

CBOE Volatility Index: VIX

checkAndCorrectData

Check that the data is set correctly and correct if not

Pick mixing weights parameters from parameter vector

reformParameters

Reform any parameter vector into standard form.

University of Michigan: inflation expectation time series: IE

quantileResiduals_int

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

change_parametrization

Change parametrization of a parameter vector

quantileResiduals

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

Function factory for formatting values

profile_logliks

Plot profile log-likehoods around the estimates

removeAllConstraints

Transform constrained and restricted parameter vector into the regular form

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

regime_distance

Calculate "distance" between two regimes

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.

Generate the covariance matrix Omega for quantile residual tests

uncondMoments_int

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

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

mixingWeights_int

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

swap_parametrization

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

Warn about large degrees of freedom parameter values

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

reformConstrainedPars

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

Calculate the number of parameters

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