Chaotic time series forecasting using deep neural networks

Abstract

This thesis focuses on time series forecasting, specifically chaotic time series, using Deep Neural Networks (DNN). The main contributions of this study can be summarized as follows: Firstly, we propose a Stacked Autoencoder-LSTM hybrid model with chaos theory for multi-step ahead forecasting of chaotic time series. Extensive analysis of five forecasting strategies shows the Multiple Input Multiple Output (MIMO) approach is most effective in leveraging inter-step dependencies and enhancing accuracy. Secondly, we introduce an LSTM forecasting methodology integrating phase space reconstruction concepts from chaos theory. Comparative evaluation evidences superior predictive performance over Deep Belief Networks on chaotic datasets. Thirdly, we present an innovative CNN-BiLSTM-GRU model combining convolutional, recurrent and gated units and chaos theory for stock market forecasting. Extensive experiments demonstrate impressive accuracy improvements compared to CNN, BiLSTM and CNN-BiLSTM benchmarks. Fourthly, we propose a novel PSR-Transformer model that integrates phase space reconstruction with the Transformer architecture. Experiments on 20-year stock market datasets show the PSR-Transformer attains higher accuracy than LSTM, CNN-LSTM and standard Transformer models for the IBM and Intel stocks. Finally, we propose a tailored ensemble framework utilizing time series segmentation, subsequence clustering using Hierarchical Agglomerative Clustering, and specialized networks for accurate localized prediction. Comparative analysis validates marked improvements over baseline methods.