Long-term prediction of chaotic time series with multi-step prediction horizons by a neural network with Levenberg–Marquardt learning algorithm

The Levenberg–Marquardt learning algorithm is applied for training a multilayer perception with three hidden layer each with ten neurons in order to carefully map the structure of chaotic time series such as Mackey–Glass time series. First the MLP network is trained with 1000 data, and then it is tested with next 500 data. After that the trained and tested network is applied for long-term prediction of next 120 data which come after test data. The prediction is such a way that, the first inputs to network for prediction are the four last data of test data, then the predicted value is shifted to the regression vector which is the input to the network, then after first four-step of prediction, the input regression vector to network is fully predicted values and in continue, each predicted data is shifted to input vector for subsequent prediction.