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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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    $\begingroup$ Why should they agree? There's not a single way to pick ARIMA orders. Everyone does it their own way. $\endgroup$ – Aksakal Mar 8 '18 at 16:14
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    $\begingroup$ ARIMA(5,1,0) is a very strange model for log return. Perhaps you made an error when using R? $\endgroup$ – Rob Hyndman Mar 8 '18 at 20:18
  • $\begingroup$ @Aksakal I genuinely thought that both use information criteria. $\endgroup$ – Anna Mar 9 '18 at 6:27
  • $\begingroup$ @RobHyndman why is a strange model? I am looking at the log returns of Bitcoin. $\endgroup$ – Anna Mar 9 '18 at 6:27
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    $\begingroup$ Log returns would normally be mean-stationary. $\endgroup$ – Rob Hyndman Mar 11 '18 at 10:10
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SPSS and 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.

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