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# How to back-transform differentiated time series data?

I have done a ARIMA forecasting via a differentiated time series data with an ARIMA (1,1,0), but the data produced by rapidminer is the differentiated data, how do I back transformed it?

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## Answers

1,635Unicorn@tftemme might be able to help out he has done a lot of the development of the series operators.

Lindon Ventures

Data Science Consulting from Certified RapidMiner Experts

1,195UnicornYou said :

via a differentiated time seriesdata with an ARIMA (1,1,0)beforefitting your data with the ARIMA (1,1,0) model ?If yes, what differentiation method have you performed on your initial time series ?

- subtraction

- logarithm

- a combination of both ?

I think it is possible to back-transform your predictions by using :

- the "cumsum" (cumulative sum) function in a Python script (in case of subtraction) - I envisage to use Python because I'm not aware of an equivalent function of "cumsum" in Rapidminer.

- the "exp" function (in case of logarithm)

- and finally a combination of "cumsum" and "exp" function in the third case above.

To conclude, as Brian said, can you give more detail about your process and your data and ideally share them ?

Regards,

Lionel

1,195UnicornI don't know why, but my intuition tells me that you used the subtraction differentiation method on your original time series.

In this case, a priori you have obtained the predictions on the differentiated data by applying the ARIMA model.

Thus you have obtained data like that :

Once you have these predictions on the differentiated data, you calculate the cumulative sum on this data and you add to this calculated time series, the first data point of your original time series - in other words, you integrate (from a mathematical point of view) your differentiated data -, and finally you retrieve the original time series with its forecast :

You can adapt the process in attached file to your own data. In my case, I used a time series called "Monthly milk production"

available in RapidMiner repository.

Hope this helps,

Regards,

Lionel

PS : This process is using a Python script, thus, you first have to :

- install Python on your computer.

- install the

Python scriptingextension from the MarketPlace.- set, in RapidMiner settings, the path where your Python.exe file is stored.

164RM ResearchTo add on the nice and detailed answer of @lionelderkrikor

ARIMA in itself performs a differentiation before fitting the model to it (the "I" in ARIMA stands for "Integrated"). The number of differentiations applied is specified by the parameter d of the (p,d,q) parameter set. So in your case it was differentiating the input series 1 time and then fitting a p=1, q=0 ARMA model to it. And when applied to perform the forecast the, the ARMA model is used to produce the forecasted values which are then integrated again automatically.

So in short you don't need to differentiate your input time series by yourself.

Another point. If you still want to integrate a differentiated time series (or any time series by the way), we will have a new Integrate operator in the upcoming 9.7.0 version of RapidMiner Studio. Besides cumulative sum, you can also apply left and right riemann sums and the trapezoidal rule to calculate the integral.

Hopes this helps

Best regards

Fabian

6Contributor II am really struggling to configure how to get back the forecasted values into the original scale as I do not want my students to use PYTHON because I am teaching them how to do analysis without any code

29Maven1Learner I1Newbie