Unsupervised machine learning (gradient boosting regression)

I still think you might benefit from studying and trying the mentioned sample workflows and the accompanying debate.

That being said: a model always predicts what input it got. So if your target is April it will predict April. That is why the data preparation went along like:

March becomes month_0
February month_1 (minus 1)
January month_2 (minus 2)

and so on. So your target would be month_0. In this example, if you now have new data March becomes month_1, February month_2 and so on. Then the prediction would be April (the new month=0).

Of course, this construction would rest on certain assumptions, especially that there is no strong seasonality since the model does not know that April ist April. If there is a seasonality you would have to tell the model that and you would need data from a previous April so the model would have a chance to assess what an April looks like in comparison to other months. In such a setting data like holidays or vacations would play a role (and think about moving holidays lik easter).

Maybe you tell us more about your data and what you want to accomplish.

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