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?
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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.