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Suppose I have a time series $Y$. I have read that an ARIMA model consists as an ARMA model of a stationarized version of $Y$.

If I try to predict $n$ ticks ahead with an ARIMA forecast model (with $n$ big), would I loose any non-stationary component of $Y$ like trend or seasonality ?

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  • $\begingroup$ No you don't, because part of the ARIMA process is reverse transforming the forecasts after they are generated. $\endgroup$
    – Skander H.
    Commented Dec 6, 2018 at 16:55

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Not if done correctly . Note non-stationarity can be (is) a symptom of a series with more than one level OR more than 1 trend OR more than 1 model error variance OR more than 1 set of model parameters OR needed Seasonal Pulses manifested/existent in the observed data.

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