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In this paper, we investigate how to represent the packet error process in a shallow water acoustic channel by means of Markov as well as hidden Markov models. To train the models, we employ experimental traces taken from transmissions performed during the SubNet'09 sea trials, off the coast of Pi-anosa island, Italy. In particular, signal-to-noise ratio (SNR) time series show significant transitions of the average SNR on a large time scale, which motivates the use of hidden Markov models. The discussion on which model best fits this experimental data is carried out considering relevant metrics for networking, i.e., packet error rate (PER), length of error bursts and correlation of errors after a given number of packet transmissions. Results show that hidden Markov models yield accurate reproduction of both first and second-order metrics.