Abstract
The daily fluctuation trends of a stock market are illustrated by three statuses: up, equal, and down. These can be represented by a neutrosophic set which consists of three functions—truth-membership, indeterminacy-membership, and falsity-membership. In this paper, we propose a novel forecasting model based on neutrosophic set theory and the fuzzy logical relationships between the status of historical and current values. Firstly, the original time series of the stock market is converted to a fluctuation time series by comparing each piece of data with that of the previous day. The fluctuation time series is then fuzzified into a fuzzy-fluctuation time series in terms of the pre-defined up, equal, and down intervals. Next, the fuzzy logical relationships can be expressed by two neutrosophic sets according to the probabilities of different statuses for each current value and a certain range of corresponding histories. Finally, based on the neutrosophic logical relationships and the status of history, a Jaccard similarity measure is employed to find the most proper logical rule to forecast its future. The authentic Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) time series datasets are used as an example to illustrate the forecasting procedure and performance comparisons. The experimental results show that the proposed method can successfully forecast the stock market and other similar kinds of time series. We also apply the proposed method to forecast the Shanghai Stock Exchange Composite Index (SHSECI) to verify its effectiveness and universality.
Highlights
It is well known that there is a statistical long-range dependency between current values and historical values at different times in certain time series [1]
We propose a novel forecasting model based on neutrosophic set theory and the fuzzy logical relationships between current and historical statuses
We propose a novel forecasting model based on high-order neutrosophic logical relationships and Jaccard similarity measures
Summary
It is well known that there is a statistical long-range dependency between current values and historical values at different times in certain time series [1]. The major points in FTS models are related to the fuzzifying of original time series, the establishment of fuzzy logical relationships from historical training datasets, and the forecasting and defuzzification of the outputs. The weight assignation model considers the differences between individual relationships, it has to deal with special relationships that appear in the testing dataset but never happen in the training dataset These FTS methods look for point forecasts without taking into account the implicit uncertainty in the ex post forecasts. We propose a novel forecasting model based on neutrosophic set theory and the fuzzy logical relationships between current and historical statuses. The remaining content of this paper is organized as follows: Section 2 introduces some preliminaries of fuzzy-fluctuation time series and concepts, and the similarity measures of neutrosophic sets.
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