Long-term prediction of time series based on stepwise linear division algorithm and time-variant zonary fuzzy information granules.

In the study of the long-term prediction of time series with high noise and nonlinearity, the trend information and fluctuation range of the sequence data is usually more valuable and practical than the forecasting of the specific values at time points. A method named as stepwise linear division (SLD) is constructed for the variable-length partition of fuzzy information granule (FIG), characteristics of which are extracted from the original data distribution of time series. Secondly, based on the above partition algorithm, a novel fuzzy information granule is first proposed, which can characterize the variant trend of the data, the range of fluctuation and the degree of dispersion. Moreover, the reliability of the prediction results can be quantified. After granulating time series, a rule-based fuzzy inference system is established to achieve the prediction of time series. Synthetic sequences and real-life time series, including chaotic Mackey–Glass time series, temperature, sunspot numbers, milk production and financial data are utilized in experiments to verify the effectiveness of the proposed scheme. The experimental results demonstrate that the proposed model can contain more rich semantic information and produce better long-term prediction performance compared with existing numeric models and fuzzy inference systems.