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I`m doing a Monthly sales forecast based on some historical data. My question is when I do the Arima(p,d,q) and then I do forecast(arima_model) in order to get the fitted values, which are nicely following the historical data points, then If I take the mean values from the forecast func, which are the n-ahead predictions, they are negative and differenced, because I do d=2 for the Arima. Is there any chance to obtain a normal values for the means from the forecast function? My aim is to know the real sales for n-ahead periods. Thank you in advance!

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  • $\begingroup$ Here is what you can do with first-order differencing: stats.stackexchange.com/questions/579328. With second-order differencing, you need to take another sum on top of of the first one. $\endgroup$ Commented Jun 20, 2022 at 13:54
  • $\begingroup$ @RichardHardy Thank you for the hints! Ive already passed by this thread, but Im not sure if it works good, because my forecasted arima values are n-ahead, so they don`t have any "undifferenced data" behind. If my data is from 50 points, the forecasted values are from 50th to 55th point. If you see what I mean by that. $\endgroup$
    – Ivan Ar
    Commented Jun 21, 2022 at 6:30
  • $\begingroup$ If you do not have the starting level (undifferenced) at time 50 and the starting difference (1st difference) at time 51, then I think it is impossible to predict the level from purely 2nd differences between 50 and 55. $\endgroup$ Commented Jun 21, 2022 at 6:35
  • $\begingroup$ @RichardHardy well If we target the fitted values of the ARIMA model which are on the differenced data, then its possible to undifference them because behind them we have the undiff data. But here Im asking about the 51-55th forecasted n-ahead values which don`t have any normal values behind. Ok thank you! $\endgroup$
    – Ivan Ar
    Commented Jun 21, 2022 at 6:47

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