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I'd appreciate some help with my data. I have to find (S)ARIMA models to fit some exportations data, but for some of them, I can't find an easy model by just looking ACF and PACF plots. So I change randomly $p,d,q$ and $P,D,Q$, but some data are really difficult to fit. Here is an example, I spent hours at modifying parameters, and don't find a good model with significant coefficients and good ACF et PACF plots of residuals. Here are pictures of time serie of exportation, and PACF (I could not post ACF because I don't have enough reputation to post more than 2 links, but nothing was significant).

enter image description here enter image description here

I am super interested if someone could give me a good model, because I feel like I will never find a good one. But I am even more interested in understanding how you find a good model for that kind of complex data. Here are the data. Thanks in advance.

- 22,04761905
- 21,36363636
- 20
- 22
- 19,19047619
- 21,81818182
- 18,68421053
- 22,9047619
- 20,38095238
- 21,27272727
- 20,68181818
- 18,6
- 17,39130435
- 19,86363636
- 18,68421053
- 20,42857143
- 19,1
- 21,2
- 19,19047619
- 21
- 19,8
- 22,52173913
- 19,52380952
- 18,52380952
- 18,7826087
- 21,9047619
- 15,45
- 23,38095238
- 22,05
- 20,57142857
- 19,5
- 18,80952381
- 18,9
- 19,86956522
- 17,55
- 18,18181818
- 22,69565217
- 19,5
- 19,23809524 
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  • $\begingroup$ what did you think? $\endgroup$ – Tom Reilly Apr 7 '16 at 20:31
  • $\begingroup$ nice work ! residuals from your model are approximately random ...thus u r good to go ! $\endgroup$ – IrishStat May 27 at 17:15
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You need to consider more than just the ACF/PACF, but the possibility that seasonality doesn't exist in all 12 months(fixed effects), but just for some(ie seasonal pulses). You also need to consider outliers (pulse) and changes in the mean(ie level shift). enter image description here

enter image description here

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