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In addition to previous answer which suggest AIC/BIC and using properties of acf/pacf plots (and their hypothesis tests) -- I would like to add that one further (more advanced) method could be to use cross validation for a time series model.


Use acf and pacf as to determine AR and MA parts. Use the position of last significant value for the two tests as the AR and MA terms respectively. or use autoarima if matlab has one with AIC or BIC coefficients. AIC returns a more general model (all possible values) while BIC results in a more constrained one (simpler).


Another possible solution is the EACF of Tsay and Tiao (1984) where the idea is that if the order of the AR process is known the MA can be inferred. The output is a table where the first left corner 0 is taken to be the order of the ARMA(p, q) model.


You want to compute the BIC (Bayessian Information Criterion) or the AIC (Akaike information criterion) for different (p,q) pairs. Here is a wikipedia article with information on how to interpret those criteria in practice. Here is a mathworks page with detailed instructions on how to perform this task within Matlab. Keep in mind that in practice and ...

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