Chaotic Time Series Prediction Using a Neuro-Fuzzy System with Time-Delay Coordinates

Abstract

This paper presents an investigation into the use of the time delay coordinate embedding technique in the multi-input-multi-output-adaptive-network-based fuzzy inference system (MANFIS) for chaotic time series prediction. The inputs of the MANFIS are embedded-phase-space (EPS) vectors preprocessed from the time series under test while the output time series is extracted from the EPS vectors. With such EPS preprocessing, the prediction accuracy of the MANFIS is found to be significantly improved. The proposed system will be tested with a periodic and the Mackey-Glass chaotic time series by comparing the prediction accuracy with and without EPS preprocessing. A moving root-mean-square error is used to monitor the error along the prediction horizon and to tune the membership functions in the MANFIS.