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I am pretty confused about the ARCH model and forecasting of stock prices / stock returns. I have read some literature about forecasting with different models (AR,MA,ARMA) and i get the concept of them and I also implemented them on a time series (of a stock price in R). Now i want to do forecasting with a ARCH model but all I can find in the literature is the forecasting of volatility of a time series but not on forecasting of the time series itself. Is it even possible to do such a forecast with the ARCH model? And if so can you explain to me how i should approach?

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  • $\begingroup$ so you want to assume the conditional mean is changing as well as the conditional variance? and you want help with the coding? I know the rugarch helps with fitting ARMA + GARCH models $\endgroup$
    – Taylor
    Commented Oct 21, 2017 at 17:47
  • $\begingroup$ My problem is, that I dont know how to compute the forecasts. For example in the AR(1) model it is Y(t)=a(0)+a(1)*Y(t-1)+e(t). For the first Forecast I simply switch the index and get Y(t+1)=a(0)+a(1)*Y(t)+e(t). But i dont know how I get these equations for the forecast in an ARCH model. $\endgroup$
    – user2968163
    Commented Oct 22, 2017 at 6:23
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    $\begingroup$ Possible duplicate of "GARCH forecasting in R: constant mean forecast!" and "Forecasting levels through GARCH model". If these are not enough, check out the other questions tagged with garch and volatility-forecasting (and arima, autoregressive, moving-average, forecasting and finance) to find out more. $\endgroup$
    – Richard Hardy
    Commented Oct 22, 2017 at 10:47
  • $\begingroup$ "What is the difference between GARCH and ARMA?" can also be helpful. $\endgroup$
    – Richard Hardy
    Commented Oct 22, 2017 at 10:51
  • $\begingroup$ I read all the links you posted and I get from them, that I need a ARMA-GARCH model to forecast my time series. The way I understand the concept of this model is, that it is very similiar to the ARMA model with the difference, that e(t) isn't a N(0,1) random variable but it is e(t)=sigma(t)*Z(t) where Z(t) is N(0,1). And sigma^2(t) can be computed based on the GARCH order. Am I right with that or have I missunderstood the model? $\endgroup$
    – user2968163
    Commented Oct 23, 2017 at 6:26

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