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I'm using auto.arima to fit my model. When I used the default CSS-ML method, I noticed that the residuals are not normal. So I want to use a method that doesn't require the normality assumption. I'm guessing CSS would work, since the method simply tries to minimize SSE but I'm not quite sure. If I use method='CSS' with auto.arima, do I still need to check for the normality of the error term with residuals?

I've tried a lot of different transformations so that the residuals can be tested as normal with jarque.bera.test or shapiro.test, but it didn't really work. The prediction results are good, Ljung-Box test shows that there is no problem with using the model, yet the normality condition isn't being satisfied. So I just want to try other approaches where normality doesn't really matter.

Richard Hardy
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statisticswannabe
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  • Could you try bootstrapping your forecasts? It seems like potentially a good way to get rid of the need for a normality assumption. – Hansel Palencia May 13 '22 at 17:33
  • Check out these threads, e.g. comments in this one. Your question might be a duplicate of one of these. – Richard Hardy May 13 '22 at 17:33
  • I checked out the comments and what prof rob hyndman said. And I actually observed that with my data, the output of method='CSS' and method = 'CSS-ML' is almost exactly the same. So I guess it is not that critical that normality assumption isn't being satisfied in this case? Am I understanding it correctly? – statisticswannabe May 13 '22 at 17:55
  • I cannot answer this definitively, as I am not sure myself. But since the ML implementation is based on an assumption of normality, it is no wonder that CSS and CSS-ML give nearly identical results. – Richard Hardy May 13 '22 at 17:58

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