I would like to ask hoy:
I i'm working in a arima model for log returns series.
Shen adjusting an ARIMA + GARCH modelo, how do i obtain the original forecast values.
That because un rugarch in r you can fit arma and Garch but, how ti integrate the forecast values?
I am not a rugarch user and I am not sure I understand your question well. rugarch seems very complex. You say you are interested in forecasts in an ARIMA+GARCH context. Of course, the presence of GARCH parameters has an influence on ARMA estimators. Maybe I am wrong but I would say that point forecasts are based only on the ARIMA model and that only forecast intervals will depend, not only on the AR and MA estimates, but also on the GARCH estimates.
What I am trying to say is if I have a model estimated as an hybrid ARIMA + GARCH, I have a point estimate give it for ARIMA and an estimate of the variance from the GARCH. But the adjustment serie is integrated in an order I = 1, then i had to use the log returns, Now, how do I get the integrated forecast for the variance because I am adjusting and forecasting over a transformed series?
If you have point forecasts and limits of forecast intervals on logs, you can back-transform them by taking exponentials. Of course the corresponding point forecasts are no longer optimal in the quadratic loss sense and the forecast intervals are no longer symmetric, see Granger and Newbold (1976) who try to improve on this in their paper on forecasting transformed series, Journal of the Royal Statistical Society. Series B 38(2), 189-203. But, assuming that your model assumptions (including the distribution of the innovations) are valid and neglecting the effect of estimation, point forecasts are medians of the distributions of the future observations and the probability of coverage of the true value is correct.
Thanks si much, i Will read about it yo understand well, if a have log (yt-yt-1) which is the transformation that i use for original serie, how i get the back transform for the variance?
I suppose you mean log(yt) - log(yt-1) because your expression has no meaning except for a strictly increasing time series. You misunderstood my answer. Do not back-transform the variance. Just compute point forecasts and interval forecasts for log(yt) using the ARIMA-GARCH model and then take exponentials of the point forecasts and the limits of the forecast intervals.
Ok, but what about the unit root problem, there's no problema with that, because the series what i adjusting is not stationary.
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