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This paper presents the prediction of financial time series using an adaptive neural network, which is called the self-organised multilayer perceptrons inspired by the immune algorithm. The simulation results were compared with the multilayer perceptrons and the functional link neural networks. The prediction capability of the various neural networks was tested on ten different data sets; the US/UK exchange rates, the JP/US exchange rate, the US/EU exchange rates, NASDAQO time series, NASDAQC time series, DJIAO time series, DJIAC time series, DJUAO time series, DJUAC time series and the oil price. We carried out two sets of experiments. In the first set, the input data are pre-processed between 0 and 1 and passed to the neural networks as non-stationary data. In the second set of experiments, the non-stationary input signals are transformed into stationary signals and passed to the neural networks. The predictions demonstrated that all neural networks generate profit using stationary data and fail to generate any profit when using non-stationary data. Furthermore, the experiment results for the stationary signals showed that the (SOMLP) outperforms the MLP neural network based on the profit. However, it produced a lower profit when predicting stock price in comparison with the Functional Link neural networks.