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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 heavy and takes advantage of parallel computing. After estimating the model, it's 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 (eigen values 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

3.1.0

License

GPL-3

Maintainer

Savi Virolainen

Last Published

June 26th, 2019

Functions in uGMAR (3.1.0)

University of Michigan: inflation expectation time series: IE

CBOE Volatility Index: VIX

Calculate gradient or Hessian matrix

Check whether all arguments are positive scalar whole numbers

Check that given object contains data

Check p and M are correctly set

checkAndCorrectData

Check the data is set correctly and correct if not

checkConstraintMat

Check the constraint matrices

change_parametrization

Change parametrization of the parameter vector

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

check_params_length

Check that the parameter vector has the correct dimension

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

get_regime_means

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

get_regime_vars

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

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

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

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

Generate covariance matrix Omega for quantile residual tests

Calculate AIC, HQIC and BIC

get_regime_autocovs

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

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

Calculate absolute values of the roots of the AR characteristic polynomials

mixingWeights_int

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

Pick mixing weights parameters from parameter vector

Calculate the number of parameters

parameterChecks

Check the parameter vector is specified correctly

Check that given object has class attribute 'gsmar'

Add random dfs to a vector

plot method for class 'gsmarpred' objects

Print method from objects of class 'gsmarsum'

print.gsmarpred

print method for class 'gsmarpred' objects

Check that the argument model is correctly specified.

Function factory for value formatting

Estimate Gaussian or Student's t Mixture Autoregressive model

Forecast GMAR, StMAR or G-StMAR process

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

removeAllConstraints

Transform constraited and restricted parameter vector into the regular form

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

quantileResiduals

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

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

Extract regime from a parameter vector

isStationary_int

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

quantileResiduals_int

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

CBOE Volatility Index: logVIX

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.

reformParameters

Reform any parameter vector into standard form.

Pick degrees of freedom parameters from parameter vector

regime_distance

Calculate "distance" between two regimes

reformRestrictedPars

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

Warn about large degrees of freedom paramater values

Create random regime

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

swap_parametrization

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

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

loglikelihood_int

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

quantileResidualPlot

Ploy quantile residual time series and kernel density

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

stmar_to_gstmar

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

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

Simulate values from GMAR, StMAR or G-StMAR process

stmarpars_to_gstmar

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

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

uncondMoments_int

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