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I would like to identify the orders p and q for ARIMA model using least squares method in Matlab. I have got also two data files (one with noise and one without)

Previously I identified p and q for AR and MA using ACF function and PACF, but now I have mixed model (ARIMA).

Could you give any tip hint how to do this?

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To identify the number of AR and MA terms you still need to look at the ACF and PACF.

To identify the orders of differencing, the easiest way is run an ARIMA model on the data with different orders of differencing (0,1,2) and with only a constant (no AR or MA term). Look at the standard deviation of these models, as well as the ACF plot - the optimal model is most likely the one with the lowest standard of deviation.

Once the identified order of differencing is taken, look at the ACF and PACF of the stationary series. In particular, look at whether the PACF or ACF cuts off sharply - if the PACF cuts off sharply start with an AR model, and vice versa. From there, look at the ACF and PACF again to determine if you need to add another term of either variety. Specifically, if there is a spike at a lower-order lag in the ACF then you should increase the MA term by 1, and vice versa.

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