# How to fit ARMA+GARCH Model In R?

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.

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I am not sure you will find a detailed example. Do you know the R package fgarch ? The garchFit() function might be useful for your task at hand cran.r-project.org/web/packages/fGarch/fGarch.pdf – edouard Jan 8 '13 at 18:00
the link here has auto.arima() doumentation cran.r-project.org/web/packages/forecast/forecast.pdf – ash Jan 8 '13 at 18:25
In practice, it is often easier to just make the AR part of the ARMA long enough so that it encapsulates however much MA the series is. This way you can just use normal regression methods instead of relying on numerical methods for ARMA. – John Jan 8 '13 at 19:00

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

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)

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If you wander about the theoretical result of fitting parameters, the book GARCH Models, Structure, Statistical Inference and Financial Applications of FRANCQ and ZAKOIAN provides a step-by-step explanation. I think that it is not a big problem to implement these steps to R.

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Here is a example of fitting Garch on financial time series. Application for regime switching in trading.