Can we use the results achieved in forecasting after employing min-max normalization on data?

Question

I am working on time series forecasting with univariate data. After applying min-max normalization, I am getting results in terms of Mean Error, Root Mean Square Error etc, less than 1 of course and close to zero. If we are to accept the results as it is, it gives us accuracy closer to 100%. But I am confused, can we use those results as it is? Kindly guide.

Answer 1

It depends on what you want to do with your forecast. I find it hard to find a use for a forecast from normalized data, so I'll assume you will denormalize the forecast before using it to base any decisions on it.

As to whether you can learn anything from the errors: if you are using the errors to understand whether your forecast is "good enough", that will likely not work on the transformed scale, since per above, the decisions you will make will be based on the back-transformed forecast. So whether your forecast is good enough will need to be judged based on the back-transformed one.

Then again, if you want to compare two forecasts A and B, you can probably do that on the transformed data, because the back-transformation is a monotone operation: the error on normalized data for method A will be smaller than for B if and only if the error is also smaller for A and B on the back-transformed forecasts.