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We consider the issues involved in model order selection for processes observed with additive Gaussian noise. In particular, we discuss conditional maximum likelihood estimation of noisy autoregressive models and provide an estimator that takes care of the observational noise. The estimator is weakly consistent, can be computed in only O(n) steps and can be used in the automatic model identification phase. Using information criteria, an extensive simulation study shows the results of order selection in the context of time and spatial series analysis.