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I have a time series of integer values $x \geqslant 0$. I would like to model it using, say, ARIMA, or Holt-Winters. How do I properly preprocess it for the task? I tried log-transform of $x' = x + 1$. Are there any other ways?

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Use a model for integer time series, not ARIMA or Holt-Winters' method. You could try an INAR for example, or an autoregressive conditional Poisson model, or a GLARMA model. See Fokianos (2012) for a comprehensive review. Some possibilities in R are described in Liboschik et al (2017).

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  • $\begingroup$ I think I could take a look at GLARMA since there is a package for that. However, is it actually conceptually wrong to model non-negative integer time series values with models like sarima or exponential smoothing (additive)? To me it seems like we can forecast, and then round to the closest integer. If the value is negative after the backwards transformation, it can be set to 0. Nevertheless, I am not sure if such a procedure is permissible given those model assumptions... $\endgroup$ – SWIM S. Jun 26 '18 at 0:20

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