# If you perform an ARMA on the volatility and add the squared returns as external variable, do you obtain a GARCH?

I wanted to focus on volatility forecasting, so instead of asking R to compute a GARCH where it would compute the errors on the returns, I wanted to model the volatility as an ARMA and add an external regressor using the argument xreg in the arima function.

I have two questions:

• Is it exactly equivalent to compute an ARMA(p,q) on the volatility with external regressors as the squared returns and to compute a GARCH (for the volatility forecast)

• Is it the correct way to do it in R ?

Tony

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As I understand that, the volatility of the process is not a stationary process itself. Even the mean is not equal to zero. So applying ARMA for volatility is not correct. Or maybe I misunderstood you? –  Dmitry Laptev Aug 20 '12 at 9:27
No you are totally correct, I think if I make the process an AR and add the squared returns, it becomes actually an EWMA –  BlueTrin Aug 20 '12 at 9:44
@Dmitry Laptev: my problem is that I wanted to filter some seasonality effect on the returns. Then I thought that dividing the returns by the seasonality curve would give me a better behaved returns series. I wanted to test my hypothesis using a GARCH model, but I do not know how to approach this problem –  BlueTrin Aug 20 '12 at 10:26