Strategies of Multi-Step-ahead Forecasting for Chaotic Time Series using Autoencoder and LSTM Neural Networks: A Comparative Study

There has been a lot of research on the use of deep neural networks in forecasting time series and chaotic time series data. However, there exist very few works on multi-step ahead forecasting in chaotic time series using deep neural networks. Several strategies that deal with multi-step-ahead forecasting problem have been proposed in literature: recursive (or iterated) strategy, direct strategy, a combination of both the recursive and direct strategies, called DirRec, the Multiple-Input Multiple-Output (MIMO) strategy, and the fifth strategy, called DirMO which combines Direct and MIMO strategies. This paper aims to propose a new deep learning model for chaotic time series forecasting: LSTM-based stacked autoencoder and answer the research question: which strategy for multi-step ahead forecasting using LSTM-based stacked autoencoder yields the best performance for chaotic time series. We evaluated and compared in terms of two performance criteria: Root-Mean-Square Error (RMSE) and Mean-Absolute-Percentage Error (MAPE). The experimental results on synthetic and real-world chaotic time series datasets reveal that MIMO strategy provides the best predictive accuracy for chaotic time series forecasting using LSTM-based stacked autoencoder.