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A Neutrosophic Forecasting Model for Time Series Based on First-Order State and Information Entropy of High-Order Fluctuation

School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, China
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
School of management, Jiangsu University, Zhenjiang 212013, China
Author to whom correspondence should be addressed.
Entropy 2019, 21(5), 455;
Received: 31 March 2019 / Revised: 26 April 2019 / Accepted: 26 April 2019 / Published: 1 May 2019
(This article belongs to the Special Issue Entropy Application for Forecasting)
PDF [821 KB, uploaded 1 May 2019]


In time series forecasting, information presentation directly affects prediction efficiency. Most existing time series forecasting models follow logical rules according to the relationships between neighboring states, without considering the inconsistency of fluctuations for a related period. In this paper, we propose a new perspective to study the problem of prediction, in which inconsistency is quantified and regarded as a key characteristic of prediction rules. First, a time series is converted to a fluctuation time series by comparing each of the current data with corresponding previous data. Then, the upward trend of each of fluctuation data is mapped to the truth-membership of a neutrosophic set, while a falsity-membership is used for the downward trend. Information entropy of high-order fluctuation time series is introduced to describe the inconsistency of historical fluctuations and is mapped to the indeterminacy-membership of the neutrosophic set. Finally, an existing similarity measurement method for the neutrosophic set is introduced to find similar states during the forecasting stage. Then, a weighted arithmetic averaging (WAA) aggregation operator is introduced to obtain the forecasting result according to the corresponding similarity. Compared to existing forecasting models, the neutrosophic forecasting model based on information entropy (NFM-IE) can represent both fluctuation trend and fluctuation consistency information. In order to test its performance, we used the proposed model to forecast some realistic time series, such as the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), the Shanghai Stock Exchange Composite Index (SHSECI), and the Hang Seng Index (HSI). The experimental results show that the proposed model can stably predict for different datasets. Simultaneously, comparing the prediction error to other approaches proves that the model has outstanding prediction accuracy and universality.
Keywords: information entropy; aggregation operator; forecasting; neutrosophic set information entropy; aggregation operator; forecasting; neutrosophic set
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Guan, H.; Dai, Z.; Guan, S.; Zhao, A. A Neutrosophic Forecasting Model for Time Series Based on First-Order State and Information Entropy of High-Order Fluctuation. Entropy 2019, 21, 455.

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