Maximum likelihood estimation of univariate Gaussian Mixture Autoregressive (GMAR),
Student's t Mixture Autoregressive (StMAR) and Gaussian and Student's t Mixture Autoregressive (G-StMAR) models,
quantile residual tests, graphical diagnostics, forecast and simulate from GMAR, StMAR and G-StMAR processes.
Also general linear constraints and restricting autoregressive parameters to be the same for all regimes are supported.
Leena Kalliovirta, Mika Meitz, Pentti Saikkonen (2015)
The goal of uGMAR is to provide tools to work with Gaussian Mixture Autoregressive (GMAR), Student's t Mixture Autoregressive (StMAR) and Gaussian and Student's t Mixture Autoregressive (G-StMAR) models. G-StMAR is such model that some of its mixture components are similar to the ones that GMAR model uses and some similar to the ones that StMAR model uses. Most importantly uGMAR provides function
fitGSMAR for two phase maximum likelihood estimation, but it also contains tools for quantile residual based model diagnostics, forecasting and simulations for example. With uGMAR it's easy to apply general linear constraints to the autoregressive parameters or to restrict them to be the same for regimes.
This is a basic example how to estimate a GMAR, StMAR or G-StMAR model to data. The data "VIX", that is used in this example, comes with the package (for details see ?VIX). The estimation process is computationally heavy and uses parallel computing.
fit12 <- fitGSMAR(data=VIX, p=1, M=2)fit12## Estimate StMAR(1, 1) model to VIX datafit11t <- fitGSMAR(data=VIX, p=1, M=1, model="StMAR")fit11t## Estimate G-StMAR(1, 1, 1) model to VIX datafit12gs <- fitGSMAR(data=VIX, p=1, M=c(1, 1), model="G-StMAR")fit12gs