Fitting ARMA-GARCH Models and Extracting Volatility Estimates in R

# How to fit ARMA+GARCH Model In R?


# 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.

## Answer by Jase (score 16)

https://quant.stackexchange.com/a/4955

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)
```

## Answer by ndhai (score 6)

https://quant.stackexchange.com/a/12650

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.

## Answer by cJc (score 6)

https://quant.stackexchange.com/a/25405

This should walk you through what you are looking for:

https://www.quantstart.com/articles/Generalised-Autoregressive-Conditional-Heteroskedasticity-GARCH-p-q-Models-for-Time-Series-Analysis

https://www.quantstart.com/articles/ARIMA-GARCH-Trading-Strategy-on-the-SP500-Stock-Market-Index-Using-R

## Answer by user1234440 (score 2)

https://quant.stackexchange.com/a/8552

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

http://systematicinvestor.wordpress.com/2012/01/06/trading-using-garch-volatility-forecast/

## Answer by Elena Sanguino (score 1)

https://quant.stackexchange.com/a/50360

I know this is an old question but I came across it when I was looking for answers for the same problem. This article was very helpful to me: http://www.rpubs.com/ddbs/gldforecasting

## Answer by Rγσ ξηg Lιαη Ημ 雷欧 (score 0)

https://quant.stackexchange.com/a/41611

GARCH模型中的ARIMA(p,d,q)参数最优化 might helps. Although it is using Chinese language, but the coding is understanable to programmers.