Prediction of Chaotic Time Series Based on LSTM, Autoencoder and Chaos Theory

Time-series forecasting, especially in a chaotic system, is a critical problem because its application is ubiquitous in several real-world fields, namely finance, environment, traffic, meteorology, industry, etc. In literature, there are many proposed methods for chaotic time series forecasting, but it is still challenging to yield a high predictive accuracy due to the chaotic characteristic which is very sensitive on the initial condition. In this work, we propose a fusion approach that takes advantage of chaos theory to represent time series data into phase space and combines autoencoder (AE) with Long Short-Terms Memory (LSTM) networks. First of all, the task of phase-space reconstruction starts with determining appropriate time lag and embedding dimension for the input time series. Next, autoencoder, which is constructed by LSTM cells, takes responsibility for latent-feature extraction through an unsupervised learning task and feeds the extracted data into LSTM-based forecaster. The experimental results on seven datasets including both synthetic and real-world chaotic time series reveal that our proposed method outperforms other forecasting methods using only stacked autoencoder, LSTM with or without chaos theory.