When I entered the above model in minitab to forecast, it said, 18 is not acceptable, and that value should be less than or equal to 5. I wonder whether it's a limitation of minitab, or this model is not acceptable. I just wanted to know whether SARIMA(3,1,18)(8,1,3) model exist.
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1$\begingroup$ This looks like some serious overfitting is going on. I've read that any term above 2 is suspicious. $\endgroup$– user2974951Commented Feb 19, 2019 at 8:42
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$\begingroup$ Yes it does over-fit, which sensed problematic. But lower parameter values fail the ljungbox test (i.e. independence of residuals). What should I do? $\endgroup$– Dovini JayasingheCommented Feb 19, 2019 at 10:48
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2 Answers
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In theory there are no bounds on the orders of an ARIMA model, other than the amount data you have (For example if your time series has 20 values, then the highest order for an AR(p) model would be p=19 - and differencing puts even more restrictions on this).
In practice, it is not recommended to go above 2 or 3 to avoid overfitting (I don't have a source for this other than conversations with colleagues and my own experiments). Additionally, automated ARIMA modeling software packages typically limit the orders of p,q,d to put bounds on the search space when searching for the best fitting model.
answered Feb 19, 2019 at 17:53
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$\begingroup$ I like to think of the ratio of parameters to data. The closer that is to unity, the higher the risk of over-fitting. I get a little panicky, and have to be tough against the approach when the ratio gets down toward 5:1. My preference is somewhere between 35:1 and 300:1. My (rude) guess is that this has something like O(100) parameters, so if there was less than O(3500) rows then I would start getting reluctant. $\endgroup$ Commented Feb 19, 2019 at 19:14
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I too have read that it is rare in economics/social science to have more than 2 levels of a given factor. But like a previous poster my question is, what if orders higher than 2 have stronger AIC (or AICc) and/or using factors lower than say 4 fail the Box-Ljung test?
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$\begingroup$ Thanks for the answer. I'm getting a negative AIC value for this. And yes, for factors lower than 4, it fails the test $\endgroup$ Commented Feb 25, 2019 at 4:40
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$\begingroup$ I am not an expert by any means in ARIMA, but I don't think you can use an ARIMA model that fails the Box-Ljung because then your error term is not Gaussian white noise which is a requirement. So you would have to take the higher AIC indicators that don't fail the test or find a new model that does not fail the Box-Ljung and has better AIC than the one you have. $\endgroup$ Commented Feb 25, 2019 at 23:14