How to fit ARMA+GARCH Model In R?

Question

I am currently working on ARMA+GARCH model using R. I am looking out for example which explain step by step explanation for fitting this model in R. I have time series which is stationary and I am trying to predict n period ahead value.

I have worked on this model but I am looking out for example where auto.arima() function is used for selecting best ARMA(p,q) based on AIC value.

Answer 1

I don't know how to select ARMA lag length when doing ARMA-GARCH. Perhaps someone can edit it into this answer.

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For the univariate case you want rugarch package. If you're doing multivariate stuff you want rmgarch. The reason these are better than other packages is threefold; (i) Support for exogenous variables which I haven't seen in any other package, (ii) support for dynamic conditional correlations, (iii) support for a huge multitude of fGARCH variants.

install.packages("rugarch")
require(rugarch)

Let's construct the data to be used as an example. Using $N(0,1)$ will give strange results when you try to use GARCH over it but it's just an example.

data <- rnorm(1000)

We can then compute the ARMA(1,1)-GARCH(1,1) model as an example:

spec <- ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1, 1), 
submodel = NULL, external.regressors = NULL, variance.targeting = FALSE), 
mean.model = list(armaOrder = c(1, 1), external.regressors = NULL, 
distribution.model = "norm", start.pars = list(), fixed.pars = list()))

garch <- ugarchfit(spec=spec,data=data,solver.control=list(trace=0))

Retrieve ARMA(1,1) and GARCH(1,1) coefficients:

garch@fit$coef

Retrieve time-varying standard deviation:

garch@fit$sigma

Retrieve standardized $N(0,1)$ ARMA(1,1) disturbances:

garch@fit$z

See what else you can pull out of the fit:

str(garch)