should the input be stationary or original for arma

Question

For this function in python, the documentation says:

statsmodels.tsa.stattools.arma_order_select_ic(y, max_ar=4, max_ma=2, ic='bic', trend='c', model_kw={}, fit_kw={})

Parameters: 
y : array-like
Time-series data

If our data is non-stationary, should we input the original time-series data here as y , or input the after differentiated stationary data? Thanks.

Answer 1

Thank you for the question, it really got me thinking. I found this explanation very helpful. Long story short: your stationary model is supposed to perform better (in terms of MSE). So, It makes sense to plug in the stationary data. Edit: Ie The differenced data