Uncertain Fuzzy Time Series: Technical and Mathematical Review

Time series consists of a sequence of observations, measured at moments in time, sorted chronologically, and evenly spaced from each other, so the data are usually dependent on each other. Uncertainty is the consequence of imperfection of knowledge about a state or a process. The time series is an important class of time-based data objects and it can be easily obtained from scientific and financial applications. Main carrier of time series forecasting is which constitutes the level of uncertainty human knowledge, with its intrinsic ambiguity and vagueness in complex and non-stationary criteria. In this study, a comprehensive revision on the existing time series pattern analysis research is given. They are generally categorized into representation and indexing, similarity measure, uncertainty modeling, visualization and mining. Various Fuzzy Time Series (FTS) models have been proposed in scientific literature during the past decades or so. Among the most accurate FTS models found in literature are the high order models. However, three fundamental issues need to be resolved with regards to the high order models. The primary objective of this paper is to serve as a glossary for interested researchers to have an overall depiction on the current time series prediction and fuzzy time-series models development.