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..