The goal of uGMAR is to provide tools to work with Gaussian Mixture Autoregressive (GMAR) and Student’s t Mixture Autoregressive (StMAR) models. Most importantly it provides function fitGMAR for two phase maximum likelihood estimation, but it also contains tools for quantile residual based model diagnostics, forecasting and simulation 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.

Simple example

This is a basic example how to estimate a GMAR or StMAR model to data. I’ll use example data “VIX” which comes with the package (for details see ?VIX). The estimation process is computationally heavy and uses parallel computing.

## Estimate GMAR(1, 2) model to VIX data
fit12 <- fitGMAR(data=VIX, p=1, M=2)

## Estimate StMAR(1, 1) model to VIX data
fit11t <- fitGMAR(data=VIX, p=1, M=1, StMAR=TRUE)

Vignette and about references

See vignette for more detailed introduction to the package and see the references for information about the models. Unfortunately there are not yet articles published considering the Student’s t Mixture Autoregressive model. This package is based on working papers considering the model and the references will be updated after the papers have been published.