Abstract: In this paper we present an efficient approach for the prediction of two sunspot-related time series, namely the Yearly Sunspot Number and the IR5 Index, that are commonly used for monitoring solar activity. The method is based on exploiting partially recurrent Elman networks and it can be divided into three main steps: the first one consists in a “de-rectification" of the time series under study in order to obtain a new time series whose appearance, similar to a sum of sinusoids, can be modelled by our neural networks much better than the original dataset. After that, we normalize the derectified data so that they have zero mean and unity standard deviation and, finally, train an Elman network with only one input, a recurrent hidden layer and one output using a back-propagation algorithm with variable learning rate and momentum. The achieved results have shown the efficiency of this approach that, although very simple, can perform better than most of the existing solar activity forecasting methods.
Abstract: In this paper, we study the application of Extreme
Learning Machine (ELM) algorithm for single layered feedforward
neural networks to non-linear chaotic time series problems. In this
algorithm the input weights and the hidden layer bias are randomly
chosen. The ELM formulation leads to solving a system of linear
equations in terms of the unknown weights connecting the hidden
layer to the output layer. The solution of this general system of
linear equations will be obtained using Moore-Penrose generalized
pseudo inverse. For the study of the application of the method we
consider the time series generated by the Mackey Glass delay
differential equation with different time delays, Santa Fe A and
UCR heart beat rate ECG time series. For the choice of sigmoid,
sin and hardlim activation functions the optimal values for the
memory order and the number of hidden neurons which give the
best prediction performance in terms of root mean square error are
determined. It is observed that the results obtained are in close
agreement with the exact solution of the problems considered
which clearly shows that ELM is a very promising alternative
method for time series prediction.