I have a data set with both x (independent variable) and y (dependent variable) are time series and I would like to use time techniques for time series regression. Butt other than blindly applying all the model and choose the when that gives me the lowest cross-validation error, is there a way to intuitively choose which model is suitable?

For clarification, I have read descriptions about some techniques to deal with this problem

i. regression with ARMA error (seems the most simplest one)

ii. ARIMAX model

iii. state space model ...

Is there any recommendation for which model to use under specific circumstances? Or are those models just equivalent? All the tutorials I read just gave me an example and then said we are going to use this model to solve it..

  • $\begingroup$ model family selection is not automated yet, there's no algorithm, just heuristics $\endgroup$ – Aksakal Nov 19 '18 at 18:02
  • $\begingroup$ @Aksakal So can I say that generally if I just choose on model from the above families and optimize the hyperparameters, it will give me an decent answer? Which is also equivalent as saying no superiority of one family over another. $\endgroup$ – Vickyyy Nov 19 '18 at 19:13
  • $\begingroup$ Unfortunately, no. $\endgroup$ – Aksakal Nov 19 '18 at 19:14
  • $\begingroup$ @Aksakal so is there any criteria or methods that guide model family selection for time series regression? $\endgroup$ – Vickyyy Nov 19 '18 at 19:15
  • $\begingroup$ Not really. I don't think there's one place where the selection is summarized in such way. For instance, ARIMA can be expressed and estimated as state space model. You also didn't even mention various filtering approaches such as hodrick prescott, exponential smoothing, error correction, cointegration etc. $\endgroup$ – Aksakal Nov 19 '18 at 19:17

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