Abstract
Most existing high-order prediction models abstract logical rules that are based on historical discrete states without considering historical inconsistency and fluctuation trends. In fact, these two characteristics are important for describing historical fluctuations. This paper proposes a model based on logical rules abstracted from historical dynamic fluctuation trends and the corresponding inconsistencies. In the logical rule training stage, the dynamic trend states of up and down are mapped to the two dimensions of truth-membership and false-membership of neutrosophic sets, respectively. Meanwhile, information entropy is employed to quantify the inconsistency of a period of history, which is mapped to the indeterminercy-membership of the neutrosophic sets. In the forecasting stage, the similarities among the neutrosophic sets are employed to locate the most similar left side of the logical relationship. Therefore, the two characteristics of the fluctuation trends and inconsistency assist with the future forecasting. The proposed model extends existing high-order fuzzy logical relationships (FLRs) to neutrosophic logical relationships (NLRs). When compared with traditional discrete high-order FLRs, the proposed NLRs have higher generality and handle the problem caused by the lack of rules. The proposed method is then implemented to forecast Taiwan Stock Exchange Capitalization Weighted Stock Index and Heng Seng Index. The experimental conclusions indicate that the model has stable prediction ability for different data sets. Simultaneously, comparing the prediction error with other approaches also proves that the model has outstanding prediction accuracy and universality.
Highlights
For stock market forecasts, summarizing the rules that can be used for future predictions from historical data is crucial
Combined with the information entropy of the m-order fuzzy-fluctuation logical relationship (FFLR) obtained in the previous step, convert the left-hands of FFLRs into neutrosophic sets according to Equation (6)
Since there is no significant difference in the effect of different error calculation methods, root mean squared error (RMSE) was chosen as the main formula for error calculation
Summary
For stock market forecasts, summarizing the rules that can be used for future predictions from historical data is crucial. Jiang et al [11] proposed a feature fusion model that is based on information entropy (IE) and probabilistic neural network, which uses IE theory to extract the characteristic entropies in vibration signals These studies inspired us to think that IE can be employed to describe the inconsistency in a period of fluctuation in a time series. High-order fuzzy time series models have been developed to describe the fluctuations in a time period and generate forecasting rules that are based on discrete high-order states for future prediction. The proposed model summarizes the discrete high-order fluctuation states to truth-membership of upper-trend, falsity-membership of upper-trend, and chaos of trends, and maps them to the three dimensions of truth-membership, falsity-membership, and indeterminacy-membership of a neutrosophic set. Inspired by the above research, we propose a prediction model based on high-order fluctuation trends and information entropy.
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