I have some difficulties to fit a GARCH model. The model input are log returns from a time series. The ouput should be the conditional variance forecast from this same time series. My problem is that when i calculate the stdev/var directly from the original time series, the scale between model output vol and original observation vol is different. This leads me to post here. The model could not be correctly specified. But i am wondering if the model output can, by definition, be used as is to forecast the observed var/stdev please.
EDIT: Let me reformulate the question as I did not receive any comment. Assuming I use price log returns (log(price t) - log(price t-1)) as an input to ARIMA-GARCH model to remove trend in the time series, can i consider the output conditonal variance to be the forecast of those same price log returns used as an input?