An Interval Type-2 Fuzzy Logic System for Stock Index Forecasting Based on Fuzzy Time Series and a Fuzzy Logical Relationship Map

Abstract

This paper proposes an interval type-2 fuzzy logic system (IT2FLS) for stock index forecasting based on a fuzzy time series and a fuzzy logical relationship map (FLRM). First, variations within the data are found with the maximum and minimum variations used for the interval settings of the universe of discourse. The time series variations are fuzzified into fuzzy sets in order to form fuzzy logical relationships, which are then used to construct the FLRM. Second, the input interval type-2 fuzzy sets (IT2FSs) and the output intervals of the IT2FLS are defined based on the maximum and minimum variations found. Third, the data variation between time t - 1 and time t, and the input IT2FSs are used as input for the IT2FLS, and the output of the IT2FLS is the forecasting variation, which is found between time t and time t + 1. An output interval is formed using the IT2FLS rule-base based on the FLRM. Finally, the forecast value at time t + 1 is defined as the data point at time t plus the forecast variation. In this paper, the proposed method is applied to data from the Taiwan Stock Exchange Capitalization Weighted Stock Index, the Dow Jones Industrial Average, and the National Association of Securities Dealers Automated Quotation. Existing methods are then compared with the proposed method using Wilcoxon non-parametric statistical testing, as opposed to simply comparing the average root-mean-square error. Based on the statistical analysis results, the proposed method is found to typically outperform the other methods.

Keywords

• Fuzzy logical relationship
• fuzzy time series
• interval type-2 fuzzy logic system
• stock index
• TAIEX