Long-Term Prediction of a Sine Function Using a LSTM Neural Network

In the past years, efforts have been made to improve the efficiency of long-term time series forecasting. However, when the involved series is highly oscillatory and nonlinear, this is still an open problem. Given the fact that signals may be approximated as linear combinations of sine functions, the study of the behavior of an adaptive dynamical model able to reproduce a sine function may be relevant for long-term prediction. In this chapter, we present an analysis of the modeling and prediction abilities of the “Long Short-Term Memory” (LSTM) recurrent neural network, when the input signal has a discrete sine function shape. Previous works have shown that LSTM is able to learn relevant events among long-term lags, however, its oscillatory abilities have not been analyzed enough. In our experiments, we found that some configurations of LSTM were able to model the signal, accurately predicting up to 400 steps forward. However, we also found that similar architectures did not perform properly when experiments were repeated, probably due to the fact that the LSTM architectures got over trained and the learning algorithm got trapped in a local minimum.