# modelling on differenced data

I have a time-series data that I want to model using machine learning models like Lasso Regression, Ridge, elastic net, etc.

However, in order to make it stationary, I difference the output variable, which is resulting in negative values being present now in the differenced data.

However, I think that differencing is having a negative effect on the preformance of my models:

With Differencing: (Yes I do realize the above-100 MAPE, however I think this is also due to the effect of having negative values in the differenced data. I know MAPE has many pitfalls, I also wish if someone could help me solve this issue)

Best Validation Scores:
R^2: 0.062
RMSE: 34.442
MSE: 1215.642
MAE: 26.633
MAPE: 231.714

Testing Scores:
R^2: 0.313
RMSE: 33.659
MSE: 1132.937
MAE: 23.688
MAPE: 215.160


Without Differencing:

Best Validation Scores:
R^2: 1.000
RMSE: 0.004
MSE: 0.000
MAE: 0.003
MAPE: 0.002

Testing Scores:
R^2: 1.000
RMSE: 0.004
MSE: 0.000
MAE: 0.003
MAPE: 0.002


I just want to know if

• this is normal or not ?
• and how to deal with differenced data ?
• is avery low RMSE (around 0) and a very high R^2 (around 1 and some cases 1) a sign of overfitting ?

Note: My dataset is small in size (154 samples). However I tried to gather more data to make it bigger, but the same thing is happening.