Learn R Programming

⚠️There's a newer version (3.5.2) of this package.Take me there.

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. The example data is simulated from a GMAR p=1, M=2 process. 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 and examine the estimates
data(simudata, package="uGMAR")
fit <- fitGSMAR(data=simudata, 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].

Copy Link

Version

Install

install.packages('uGMAR')

Monthly Downloads

392

Version

3.2.5

License

GPL-3

Maintainer

Savi Virolainen

Last Published

April 4th, 2020

Functions in uGMAR (3.2.5)

Add random dfs to a vector

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

Check whether all arguments are stricly positive natural numbers

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

change_parametrization

Change parametrization of a parameter vector

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

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

Calculate gradient or Hessian matrix

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

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

check_params_length

Check that the parameter vector has the correct dimension

Check that p and M are correctly set

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

Check that given object has class attribute 'gsmar'

Check that given object contains data

Check that the argument 'model' is correctly specified.

checkConstraintMat

Check the constraint matrices

checkAndCorrectData

Check that the data is set correctly and correct if not

Condinional mean or variance plot for GMAR, StMAR, and G-StMAR models

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

Calculate AIC, HQIC and BIC

Function factory for formatting values

Generate the covariance matrix Omega for quantile residual tests

get_regime_vars

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

get_regime_means

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

Calculate absolute values of the roots of the AR characteristic polynomials

Extract regime from a parameter vector

Estimate Gaussian or Student's t Mixture Autoregressive model

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

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

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

Calculate the number of parameters

parameterChecks

Check the parameter vector is specified correctly

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

loglikelihood_int

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

mixingWeights_int

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

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

get_regime_autocovs

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

profile_logliks

Plot profile log-likehoods around the estimates

quantileResidualPlot

Plot quantile residual time series and histogram

Print method from objects of class 'gsmarsum'

print.gsmarpred

Print method for class 'gsmarpred' objects

Pick mixing weights parameters from parameter vector

Pick degrees of freedom parameters from a parameter vector

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

Pick phi0 or mean parameters from parameter vector

isStationary_int

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

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

quantileResiduals_int

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

Plot method for class 'gsmarpred' objects

reformConstrainedPars

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

Create random regime parameters

reformParameters

Reform any parameter vector into standard form.

randomIndividual

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

Forecast GMAR, StMAR, or G-StMAR process

reformRestrictedPars

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

regime_distance

Calculate "distance" between two regimes

removeAllConstraints

Transform constrained and restricted parameter vector into the regular form

stmar_to_gstmar

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

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

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

randomIndividual_int

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

Create random AR coefficients

swap_parametrization

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

uncondMoments_int

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

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

stmarpars_to_gstmar

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

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

Warn about large degrees of freedom parameter values

quantileResiduals

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

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

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