Which arma model is best one? I am studying ARMA models. 
ARMA(25,25) or ARMA(1,1) which one better model? 
Why? I think that the reason is the ommission of irrelevant variable 
 A: There is no general answer the question of how good a model is as it depends on your problem. A model is generally used to fit your underlying problem structure.
If you data exhibits non periodic dependence up to 25 time steps back in both autocorrelation and partial autocorrelation it might be so that you'll need an ARMA(25,25) but my general guess would be that this is not the case and that you just selected a high model order. In this case it will just overfit to the data and you will lose accuracy. This means that you will start to model the underlying noise so that the model is skewed to fit the data used for parameter inference too well. This will lead to worse predictions on future data which is not available at the time of parameter estimation. 
Let me draw an analogy to regression as it is very similar but a lot easier to show. Consider that you have a Linear relationship between your target and covariates. Using a polynomial of order 25 instead of 1 as a fit to your data will not improve the predictions on future data. On the contrary it will most probably be a lot worse as you blow up your problem to a lot bigger proportions.
Take this plot as an example. Here a polinomial of order 5 is fitted to data of order 2. It is easy to spot how the higher order polinomial is overfitted to the random noise in the training set. (The true distribution is shown in grey in the background)
 
The same holds for ARMA processes. If you choose a model of very high order you will not get better predictions, only a closer fit yo your noise. 
You therefore need to make sure you use a model of the right order to get good predictions. There are several ways to do this. A simple method to get a pointer in the right direction is look at the extended sample autocorrelation function (ESACF).
If you want a model that does not put any assumptions on your data you need to resort to non-parametric statistics but then again, if your model assumptions are correct you will gain on enforcing them. 
