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I cannot say I am very familiar with ARMA (I must admit that I am kind of biased to begin with, so for a long time, I haven't tried to bother with AR/MA-like linear models).

However, for some reason, I tried ARMA to solve problems of forecasting the behavior of some very complicated dynamic systems, and I found ARMA models work very well, much better than most of the modelling methods I am familiar with.

However, looking at the method, it seems that there is nothing particularly special about these kinds of time series models, like OLS, regression, MLE etc, and it looks like theoretically speaking it is even very limited comparing to nonlinear models.

So what do you think makes AR/MA work better than many more general models? the properties of stationary processes? MLE? The use of some information theory in training?

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  • $\begingroup$ "What you think" is perhaps badly phrased. This way, it makes this question solely opinion-based. $\endgroup$ – Firebug Sep 19 '17 at 22:52
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ARIMA models can easily be enhanced to include

  1. incorporation of Pulse , level shifts , local time trends and seasonal pulses
  2. lag and lead structures for user-specified causals
  3. incorporation of variance changes
  4. incorporation of parameter changes
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It depends on your research question.

  1. Are you forecasting a multivariate time series model ?

  2. Are you trying to forecast a univariate time series model ?

  3. Are you trying to implement this in excel to share results with executives that may not understand ARIMA/ARMA.

From my experience working with ARIMA models is that it is very powerful to answer specific questions. Much much better than OLS or other regression techniques since it not only takes into account the moving average component it also takes care of the auto regressive portion.

In many cases most time series are affected by other variabes and i strongly recommend using VARMAX in that case if you have that kind of data.

http://support.sas.com/documentation/cdl/en/etsug/63348/HTML/default/viewer.htm#etsug_varmax_sect001.htm You can now do this in other packages as well.

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