Differential Heuristic Information-based Fuzzy Time Series Forecasting Model

Time series are an important kind of complex data object. Through further analyzing and processing time series in the domain, such as society, economy, science and technology, people may reveal the inherent laws of movement, change and development of things in the real world. The effective and precise analysis, therefore, undoubtedly has an extremely pivotal and far-reaching significance to the development of social economy, science and technology and more.Financial market, as part and parcel of economic system, has been considering an indispensable part of all countries. The research of forecasting, analyzing, and controlling the financial time series, accordingly, has become the basic work in the fields of finance and economy. Due to among the several characteristics of financial time series are such crucial issues as nonlinearity, vagueness and existence of linguistic value, financial time series forecasting has been regarded as the most challenging applications of the analysis of modern time series.Recently, the study of fuzzy time series has increasingly attracted much more attention owing to its outstanding capacities of dealing with the uncertainty and vagueness which are embodied in the observation data collected. However, how to partition the universe of discourse objectively so as to determine effective lengths of intervals and how to construct the matrix of fuzzy logic relationship effectually are still unsolved completely. In the paper, therefore, the author probes into these two aforementioned questions in the modeling of fuzzy time series. The main findings have been made in the following aspects.1) In order to employ the embodied trends in historical data effectively and describe the fuzzy logic relationships of observations, this paper proposed a difference heuristic model of fuzzy time series. According to the difference with different order among the historical data, this operator is used to construct three matrixes of fuzzy logic relationships integrated the adaptive capability. Through forecasting the typical stock indexes, such as Dow Jones Industrial Average, Hang Seng index and Nikkei 225, and daily price of USD/JPY exchange rate, the empirical results show that the proposed model is able to obtain higher forecasting rates than the counterpart of existing models; and 2) This paper proposed a novel model of fuzzy time series based on K-means clustering algorithm and illustrated its procedure of modeling, correspondingly. The model used clustering centers of classification instead of the midpoints of each interval used in numerous existing models. The universe of discourse, consequently, will be partitioned objectively, relatively speaking. Furthermore, this method also modified the fuzzified values correspondingly by using the clustering centers obtained. Moreover, taking the enrollments of the University of Alabama as a dataset, the forecasting results demonstrated that the proposed method provides higher forecasting accuracy rate than the excising ones.