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.
You can install the released version of uGMAR from CRAN with:
And the development version from GitHub with:
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))