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My data is not normal and I have tried Box-Cox transformation, yet after Box-Cox transformation, it still fails under the Kolmogorov-Smirnov test, so can I skip the normality transformation and use the raw data to do SARIMA forecasting?

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The original data does not need to be normal BUT the residuals need to be normal in order to formally perform tests of significance of estimated parameters. Sometimes the variance of the errors changes of time and there maybe a need to consider using weighted estimation or a power transform via the Box-Cox test http://stats.stackexchange.com/questions/18844/when-and-why-to-take-the-log-of-a-distribution-of-numbers .

Outliers can often give you the impression of non-normality and this can be treated by identifying and including deterministic structure as suggested by http://faculty.chicagobooth.edu/ruey.tsay/teaching/uts/lec10-08.pdf and http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html.

If you wish to post your data , I will try and help you further.

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