ARIMA grid search for best $p$, $d$, $q$ orders based on BIC metric

Question

i am new to R, and i was hoping to get some answers to some questions i have

1. is there a function to loop through a range of ARIMA model to get the best order/seasonal based on BIC/AIC ?
2. do i have always to difference the data if its not not stationary or there might be another reason to that and i dont have to take the differencing ?
3. i used Auto ARIMA to find the best ARIMA model based on its BIC, and i specifically specified BIC perimeter in the Auto ARIMA function but when i tried to use some candidate ARIMA order i was able to get a lower BIC than what the Auto ARIMA got, how is that possible ?
4. what could be a better practice, to use the differencing time series data in the arima function , or to use the original one and specify that there is an order of d there?

Answer 1

1. Yes. Use forecast::auto.arima(data, ic="bic")
2. No. auto.arima() will determine the number of differences needed for you.
3. auto.arima() will avoid models which could be numerically unstable. For example, the fitted model could have near unit-roots.
4. Over-riding the automatic selected order of differencing is sometimes useful. But make sure you are aware of the consequences. See https://otexts.com/fpp2/arima-r.html#understanding-constants-in-r