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I am using the fGARCh package in R to analyze volatility of stock returns. More precisely I am using a garch(1, 1) fit. The code looks like this:

GARCH11<-garchFit(formula = ~garch(1, 1), data = Returns.zoo, trace = FALSE)

Returns.zoo is my time series.

Now I know the interpretation of GARCH@h.t and GARCH@sigma.t. But what does GARCH@fitted tell me in relation to the time series and why is the value equal at all times?

I would be very relieved if someone could enlighten me. Thanks very much!

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When fitting a volatility model, you have two series - one describing the actual data and one the data's volatility.

In your code, the volatility part is modelled by a GARCH(1,1) model, while the data is simply modelled with a constant term, which is included by default. Hence, your "fitted" model is just a constant term and GARCH1@fitted provides a constant value, which is equal to the mean coefficient mu.

If you additionally want to model the data series, you can add an ARMA model to your specification:

GARCH11<-garchFit(formula = ~arma(1,1)+garch(1, 1), data = Returns.zoo, trace = FALSE)

Then, the @fitted output will be time-varying, following an ARMA(1,1) process. As you said that you model stock returns, using an ARMA model probably isn't necessary, though.

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