Abstract: A time series that is established by a measured signal of a dynamic system, for example a quotation curve on the stock market, is modelled according to its probability density in order to be able to make a prediction of future values. A non-linear Markov process of the order m is suited for describing the conditioned probability densities. A neural network is trained according to the probabilities of the Markov process using the maximum likelihood principle, which is a training rule for maximizing the product of probabilities. The neural network predicts a value in the future for a prescribable number of values m from the past of the signal to be predicted. A number of steps in the future can be predicted by iteration. The order m of the non-linear Markov process, which corresponds to the number of values from the past that are important in the modelling of the conditioned probability densities, serves as parameter for improving the probability of the prediction.