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I am using R, and I have a time series with both positive and negative values. It is stationary but non-normal. Acf, pacf and auto. arima suggest a MA(1) model. I fit this, and the residuals are again non- normal and also suggest MA(1).

  1. Is there some procedure to determine best transformation for the time series?

  2. I am bit confused about how to choose the arima method (maximum likelihood or conditional sum-of-squares).

Many thanks!

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  • $\begingroup$ Why are non-normal residuals a problem? $\endgroup$
    – Rob Hyndman
    Commented Jun 27, 2021 at 23:07
  • $\begingroup$ I think that the assumption for residuals are necessary for an arima model to be acceptable, isn't that so? $\endgroup$
    – Irene
    Commented Jun 27, 2021 at 23:44
  • $\begingroup$ No. It is not necessary. It is often assumed when producing prediction intervals, but even then it is not necessary as you can bootstrap the residuals when producing prediction intervals. $\endgroup$
    – Rob Hyndman
    Commented Jun 28, 2021 at 0:52
  • $\begingroup$ Thank you for your reply! How about the time series? Should it be transformed to normal before fitting arima? $\endgroup$
    – Irene
    Commented Jun 28, 2021 at 0:58
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    $\begingroup$ The purpose of transformations with ARIMA models is usually to deal with heteroskedasticity. If the variance increases with the level, a transformation may be required. See otexts.com/fpp2 or otexts.com/fpp3 to learn about ARIMA modelling. $\endgroup$
    – Rob Hyndman
    Commented Jun 28, 2021 at 2:21

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