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My annual time series has following ACF/PACF structure.

enter image description here

Based on what ARIMA model should be selected here? Exponential decreasing of ACF --> AR(4) probably? Or because of periodical ACF maybe SMA? Or because of signifiant 1st and 8th PACF --> SAR? Or because it is an annual time series I should not consider seasonal models? What is the best approach here, please?

Time series is stationery.

Time series plot: enter image description here

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    $\begingroup$ Your ACF has a periodicity of length about 10. Is there a reason to suspect a recurring seasonal cycle of length 10 in your data? If so, SARIMA looks like a good bet. Failing that, I would trust a modern approach using information criteria (as implemented, e.g., in forecast::auto.arima() for R) much more than the Box-Jenkins approach. $\endgroup$
    – Stephan Kolassa
    Commented May 7, 2021 at 9:00
  • $\begingroup$ Yeah it seems so. I added time series plot. If I remember correctly, our teacher said that we should consider using seasonal models only if we have montly or quarterly time series - that is why I am not sure if it is possible to use it also for yearly time series. $\endgroup$
    – romanzdk
    Commented May 7, 2021 at 9:03
  • $\begingroup$ What does this data represent? Is there some natural reason for an approx 10 year cycle? Maybe look into spectral analysis ... $\endgroup$
    – kjetil b halvorsen ♦
    Commented May 8, 2021 at 16:28
  • $\begingroup$ Yeah, the data is from here encyclopediaofmath.org/wiki/Canadian_lynx_data $\endgroup$
    – romanzdk
    Commented May 9, 2021 at 9:41

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