title: Get back original prediction from logged and differenced time-series data in python
body: <p>I am doing time-series forecasting to predict future orders. Since the data was non-stationary I did log and first-differencing. then I trained the Arima Model using the order values I got from auto_arima by passing the log-differenced data. I used last 30 days for testing and rest for training. I am getting the predicted values in the logged and differenced format. also I predicted for next 30 days which is not present in the dataset which give prediction in same format. How to get back the original data in both the cases since I don't have the data of future 30 days.</p>
  <p><a href="https://i.stack.imgur.com/CGr8O.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/CGr8O.png" alt="logging" /></a>
  <a href="https://i.stack.imgur.com/CcbhD.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/CcbhD.png" alt="differencing" /></a></p>
  <p><a href="https://i.stack.imgur.com/Yqkzh.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Yqkzh.png" alt="Prediction for testing data" /></a></p>
  <p><a href="https://i.stack.imgur.com/oUvFC.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/oUvFC.png" alt="Prediction for future" /></a></p>