Multi-Scale Analysis of Time Series Based on a Neuro-Fuzzy-Chaos Methodology Applied to Financial Data

Abstract

Integration of neuro-fuzzy and chaos tools of time series analysis is the topic of this work. In our approach, the time series is considered as a multi-level process evolving over time. Prediction is implemented as a hierarchical process when the higher-level trends are predicted first, followed by the lower level values of the time-series. This treatment may help to challenge the view that a chaotic process is not predictable in a long time, as long-term prediction could be possible for certain types of chaotic time series as a cascade of approximations with increasing accuracy. After the initial time series analysis, a corresponding hierarchical multi-modular structure is built to model the time series at different levels. A fuzzy neural network FuNN is used for the purpose of building each of the modules in the modular structure. Fuzzy rules for explaining chaotic time series at different levels of its behavior can be extracted. A case study of a stock index time series has been used through the paper to illustrate the proposed methodology and techniques.