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This paper introduces a method to model the rapid attenuation fluctuations (the scintillation) on satellite links with generating the time series of attenuation levels. The applied model is a hidden Markov model which is parameterized from an appropriate filtered Gaussian white noise signal. For the parameterization of the Markov chain the Baum-Welch expectation-maximization algorithm has been used. The resulting Markov model is applicable to generate scintillation time series for any desired duration with the time and amplitude resolution of the original training data. From the synthesized time series the statistical properties like the cumulative distribution and the dynamics of the scintillation can be also determined. To prove the accuracy of the model at first the cumulative distribution function of the original and synthesized time series are compared. A further test of the model validity is the comparison with real scintillation measurement on a land mobile satellite link. Finally, the spectral test of the filtered Gaussian model, the hidden Markov model and the satellite link measurement shows that the constant and decreasing parts in the periodograms are showing similarities what confirms the good quality of the model.