'Transform the double differenced forecast to original time-series

I am working on the ARIMA model for time-series forecasting. As my time-series is indicating non-stationary, I have transformed the data to stationary by double differencing (differenced two times). Now I have successfully fit the model and to get a good forecast I need to transform my datasets back to the original signal.

I am not getting how to do that. Please help me with possible solutions.

Thank you

Solution 1:^[1]

You can use this method below to inverse differencing and just call it twice. You must recall the first value of the series before differencing:

def inverse_diff(series, last_observation):

    series_undifferenced = series.copy()

    series_undifferenced.iat[0] = series_undifferenced.iat[0] + last_observation

    series_undifferenced = series_undifferenced.cumsum()

    return series_undifferenced

inverse_1 = inverse_diff(your_differenced_series, first_value_of_differenced_series)
inverse = inverse_diff(inverse_1, first_value_of_original_seires)

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Solution 1	Arne Decker

'Transform the double differenced forecast to original time-series

Solution 1:[1]

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Solution 1:^[1]