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I am a beginner of the R software v.3.2.5.

I fitted a hybrid ARMA+GARCH stochastic model to a sample of log-returns on an exchange rate using the rugarch package functions. The fitted(modelfitNUMBER) option returns the fitted values in terms of log-returns. So my question is:

How can I convert those fitted log-returns back to exchange rates using R and/or Excel?

Is it correct to run the following: exp(fittedlogreturn-t)*actualexchangerate-t-1?

I already browsed through many posts on this topic but found nothing enlightening.

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  • $\begingroup$ I do not know if taking exp(fittedlogreturnt)*actualpricet-1 is correct $\endgroup$ – msmna93 Sep 3 '16 at 15:19
  • $\begingroup$ So what function call did you use to convert the returns into logs in the first place? $\endgroup$ – dww Sep 3 '16 at 15:28
  • $\begingroup$ In the first place, I used this function diff(log(exchangerates)) to get the log-returns. Those logreturns are then fitted with the modelfit function of the rugarch package. $\endgroup$ – msmna93 Sep 3 '16 at 15:30
  • $\begingroup$ Log gives natural logs, so yes, exp is the correct inverse function $\endgroup$ – dww Sep 3 '16 at 15:31
  • $\begingroup$ yes thanks. But my real doubt was on the kind of price that I need to multiply to the exponential of log-returns. Should this price be the one from the actual(observed series)? $\endgroup$ – msmna93 Sep 3 '16 at 15:32

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