Predicting credit applications with timeseries
Intuitively I think that the model would need some additional features based on the economic context in order to be more accurate, and that would also be a part where the evolution across time really matters.


  
  Would it now be a good idea to create train/test folds based on theclient_nr? Or should I make splits by month?
  


If possible you need to have a full time series for a client as an instance, so I'd say splitting on the client number is much better. But select the client numbers randomly from the full set of client ids, because it's possible that the clients number are assigned following a particular order in time.


  
  Should I then select the first $n$ months as features, and create one label from $k$ months after $n$ that indicates whether the client has applied for a credit in those $k$ months? Or is there a better way?
  


That depends on the exact goal and on the kind of algorithm being used, but afaik usually with a time series the label is predicted at any given time given the past and current features and the past labels (or past predicted labels).


  
  Would it be better to use regression using nr_credit_applications, or classification on credit_application?
  


This is more a matter of convenience for your application or for the algorithm being used, as the accuracy should be very similar (assuming you use the same kind of method of course).