Long-term forecasting of time series based on linear fuzzy information granules and fuzzy inference system

Long-term time series forecasting is a challenging problem both in theory and in practice. Although the idea of information granulation has been shown to be an essential concept and algorithmic pursuit in time series prediction, there is still an acute need for developing a sound conceptual framework for time series prediction so that information granulation can capture the essence of collections of data better, including average and trend information. In this paper, a novel type of fuzzy information granule involving a time-dependent (non-stationary) membership function is proposed to structure numerical time series into granular time series. We show that the underlying arithmetic along with the concept of distance for this type of information granules can be expressed in a simple way, which facilitates the ensuing processing of information granules. With this regard, distances between observation granules and antecedent granules presented in fuzzy rules can be easily determined. The design of long-term prediction method based on fuzzy inference system is then realized through interpolation completed with the aid of fuzzy rules. Experiments involving chaotic Mackey-Glass time series and real-world time series demonstrate that the proposed model produces better long-term forecasting than some existing numeric models such as Autoregressive (AR) models, nonlinear autoregressive (NAR) neural networks, Support Vector Regression (SVR) and fuzzy inference systems involving triangular and interval information granules.