I am trying to find the best model for a log return time series. In SPSS the expert modeller is stating that an ARMA(0,0,0) is the best while in R the best fit is (5,1,0).
Why don't they agree on the same model?
auto.arima() probably use very different criteria for model selection.
auto.arima() searches heuristically over the space of possible models, attempting to minimize an information criterion. I don't know how SPSS decides on a model (but see this), and I strongly suspect that the algorithm is different - it may minimize one-step ahead forecast errors instead of information criteria, or a different IC than
auto.arima(), or it may even have the same target function, but iterate through the models differently and end up in a different local optimum.