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I have often found comments that no MA, AR or integration in ARIMA should have a value beyond 2 in social science data. So what do you do if your ARIMA analysis suggest one of these beyond 2? I assume you chose a reduced model, I m not sure how you do this.

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There are conventions, rules of thumb, pieces of hard-won experience and whatever you want to call them in many places, in science and elsewhere. If you believe your situation warrants crossing a line that is usually not crossed, you should (a) make double sure you do need to cross that line, and (b) write up a compelling argument for why.

In your particular case, I would suggest first fitting a model with orders restricted to be no larger than 2, then another model with larger potential orders. Then report the AICs. There are a couple of rules of thumb about differences in AIC, e.g., in Burnham & Anderson. If the unresticted model has an AIC that is lower than the AIC of the restricted model by 10, then this is quite an argument. If the unrestricted model improves the AIC by only 0.3, the argument is less convincing. Alternatively, use a holdout sample and see which model yields lower forecast errors. (Are orders relatively stable if you remove observations at the end? If the model is stable, that is another point in its favor.)

Related: Order of ARMA models and Why does default auto.arima stop at (5,2,5)?

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  • $\begingroup$ Thank you. There is little theory and almost no time series in the field I work in (vocational rehabilitation particularly spending) so its unlikely I will ever have a good basis to reject the rules of thumb. Historically I used various exponential smoothing models (Holt, Winters etc) now I am trying ARIMA and UCM for the first time. There are automated searches in SAS, I was not sure hat to do if they suggest parameters beyond 2 . I knew about the use of AIC tests to chose models, but never considered that approach. Is AIC better or AICc. I usually work with about 50 months of data. $\endgroup$
    – user54285
    Commented Apr 30, 2019 at 0:37
  • $\begingroup$ AICc is better for "small" amounts of data. With 50 data points, there is not all that much of a difference. I would perhaps prefer AICc. $\endgroup$ Commented Apr 30, 2019 at 4:08
  • $\begingroup$ @StephanKolassa, if AICc is a higher-order approximation than AICc (is that right?), there should be no reason to ever prefer AIC, unless AICc is more difficult to calculate (which it is not to any reasonable degree). $\endgroup$ Commented May 2, 2019 at 11:04
  • $\begingroup$ @RichardHardy: true. It's just that for larger samples, the difference is often minuscule, especially since we mostly care about differences in AIC/AICc between different models. $\endgroup$ Commented May 2, 2019 at 11:34
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In my experience studying ARIMA models (51 plus years ) , the phenomena of >2 polynomials either ar/ma or differencing usually suggests/indicates a Gaussian Violation of some sort .

Gaussian violations can be caused by a violation in the expected value or the variance of the errors. Common treatments are Intervention Detection Intervention Analysis Coding in R TSA Package & http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html and power transforms http://stats.stackexchange.com/questions/18844/when-and-why-to-take-the-log-of-a-distribution-of-numbers OR http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html

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  • $\begingroup$ thank you. In honesty I have paid less attention to violations of assumptions in ARIMA other than the box ljung test then say regression. The ARIMA literature I have looked at rarely if ever brings them up. I will in the future. $\endgroup$
    – user54285
    Commented Apr 30, 2019 at 0:28

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