TAIEX forecasting based on fuzzy time series, particle swarm optimization techniques and support vector machines

doi:10.1016/j.ins.2013.06.005

Information Sciences

Volume 247, 20 October 2013, Pages 62-71

https://doi.org/10.1016/j.ins.2013.06.005 Get rights and content

Highlights

•
A new method for forecasting the TAIEX is presented.
•
It forecasts the TAIEX based on fuzzy time series, particle swarm optimization techniques and support vector machines.
•
The particle swarm optimization techniques are used to get optimal intervals in the universe of discourse.
•
The support vector machine is used to classify the training data set.
•
The experimental results show that the proposed method outperforms the existing methods for forecasting the TAIEX.

Abstract

In this paper, a new method for forecasting the TAIEX is presented based on fuzzy time series, particle swarm optimization techniques and support vector machines. The proposed method to forecast the TAIEX is based on the slope of one-day variation of the TAIEX and the slope of two-days average variation of the TAIEX. Because the slope of two-days average variation of the TAIEX is smoother than the slope of one-day variation of the TAIEX, it is chosen to define the universe of discourse. The particle swarm optimization techniques are used to get optimal intervals in the universe of discourse. The support vector machine is used to classify the training data set. The first feature and the second feature of the support vector machine are the slope of one-day variation and the slope of two-days average variation of the TAIEX, respectively. The experimental results show that the proposed method outperforms the existing methods for forecasting the TAIEX.

Introduction

Fuzzy time series has successfully been used to deal with various forecasting problems, such as to forecast the temperature, the economy, the inventory, the earthquake, and the stock index. In [28], Song and Chissom proposed the concepts of fuzzy time series. In [29], [30], Song and Chissom presented the time-invariant fuzzy time series model and the time-variant fuzzy time series model to forecast the enrollments of the University of Alabama. In recent years, some fuzzy forecasting methods based on fuzzy time series have been presented [2], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [23], [24], [25], [26], [27], [31], [32], [33], [34], [35], [36]. In [2], Chen and Chen presented a method used multivariate to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) [39]. In [4], Chen presented a high-order fuzzy time series model for forecasting the enrollments of the University of Alabama to get higher forecasting accuracy rates. In [6], Chen and Chen presented a method to forecast the TAIEX by fuzzy variation groups. In [7], Chen and Chung presented a method for forecasting the enrollments of the University of Alabama using fuzzy time series and genetic algorithms. In [8], Chen and Hsu presented a method to forecast the enrollments of the University of Alabama based on fuzzy time series. In [9], Chen and Hwang presented a two-factors time-variant fuzzy time series model to predict the temperature. In [11], Chen et al. presented a method for fuzzy forecasting based on two-factors high-order fuzzy-trend logical relationship groups and particle swarm optimization techniques. In [12], Chen and Wang presented a high-order fuzzy time series forecasting method using fuzzy-trend logical relationships. In [13], Chen and Wang presented a method for forecasting the enrollments of the University of Alabama by using automatic clustering techniques and fuzzy logical relationships. In [15], Huarng observed that the length of intervals in the universe of discourse can affect the forecasting results and proposed the distribution-based length method and the average-based length method for handling the forecasting problems. In [16], Huarng presented a method using a heuristic function to forecast the enrollments of the University of Alabama and the Taiwan Futures Exchange (TAIFEX). In [17], Huarng and Yu presented a method using type-2 fuzzy time series to forecast the TAIEX. In [36], Teoh et al. presented a method to forecast the stock markets based on a hybrid multi-order fuzzy time series model, which employed the rough set theory to mine fuzzy logical relationships from time series. In [14], Hung and Lin developed a novel intuitionistic fuzzy least-squares support vector regression with genetic algorithms to forecast the long-term indexes of business cycles. In [26], Lin et al. developed a fuzzy least-squares support vector regression model with genetic algorithms to forecast seasonal revenues. However, because the forecasting accuracy rates of the existing methods are not good enough, a new method is needed to be developed to overcome the drawback of the existing methods to get higher forecasting accuracy rates.

In this paper, a new method for forecasting the TAIEX is presented based on fuzzy time series, particle warm optimization techniques [22] and support vector machines [37]. The proposed method to forecast the TAIEX is based on the slope of one-day variation of the TAIEX and the slope of two-days average variation of the TAIEX. Because the slope of two-days average variation of the TAIEX is smoother than the slope of one-day variation of the TAIEX, it is chosen to define the universe of discourse. The particle swarm optimization techniques are used to get optimal intervals in the universe of discourse. The support vector machine is used to classify the training data set. The first feature and the second feature of the support vector machine are the slope of one-day variation and the slope of two-days average variation of the TAIEX, respectively. The experimental results show that the proposed method outperforms the existing methods for forecasting the TAIEX.

Section snippets

Fuzzy time series

In this section, some basic concepts of fuzzy time series are reviewed from [3], [28], [29], [30], where the values of fuzzy time series are represented by fuzzy sets [38]. Let U be the universe of discourse, where U = {u₁, u₂, … , u_n}. A fuzzy set A_i in the universe of discourse U can be represented by $A_{i} = f_{A_{i}} (u_{1}) / u_{1} + f_{A_{i}} (u_{2}) / u_{2} + \dots + f_{A_{i}} (u_{n}) / u_{n},$ where $f_{A_{i}}$ is the membership function of the fuzzy set A_i, $f_{A_{i}} (u_{j})$ denotes the degree of membership of u_j belonging to the fuzzy set A_i, $f_{A_{i}} (u_{j}) \in$ [0, 1] and 1 ⩽ j ⩽ n.

Particle swarm optimization

In [22], Kennedy and Eberhart developed an optimization algorithm, named particle swarm optimization (PSO), which was inspired by the social behavior of bird flocking or fish schooling. In PSO, a set of particles consists of a particle swarm, where a particle denotes a potential solution. The position and the velocity of the ith particle in an n-dimensional search space can be represented by X_i = [x_i,1, x_i,2, … , x_i,n] and V_i = [v_i,1, v_i,2, … , v_i,n], respectively. Each particle has the personal best

A new method for forecasting the TAIEX based on fuzzy time series, particle swarm optimization techniques and support vector machines

In this section, a new method to forecast the TAIEX is presented based on fuzzy time series, particle swarm optimization techniques and support vector machines. The proposed method is now presented as follows:

Step 1: Let V1_t denote the variation between trading day t and trading day t − 1 and let V2_t denote the average variation between trading day t and trading day t − 2, respectively, shown as follows: $V 1_{t} = {TAIEX}_{t} - {TAIEX}_{t - 1},$ $V 2_{t} = ({TAIEX}_{t} - {TAIEX}_{t - 2}) / 2,$ where TAIEX_t−2, TAIEX_t−1 and TAIEX_t denote the TAIEX

Experimental results

In this section, the proposed method is applied to forecast the TAIEX from 1990 to 2004. In order to compare the experimental results of the proposed method with the ones of the methods presented in [3], [5], [6], [10], [16], [18], [24], [30], [31], a 10 month/2 month split for training/testing is also adopted, i.e., for each year, the data from January to October are used as the training data set, and the data from November to December are used as the testing data set. The Root Mean Squared

Conclusions

Acknowledgement

This work was supported in part by the National Science Council, Republic of China, under Grant NSC 101-2221-E-011-171-MY2.

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TAIEX forecasting based on fuzzy time series, particle swarm optimization techniques and support vector machines

Highlights

Abstract

Introduction

Section snippets

Fuzzy time series

Particle swarm optimization

A new method for forecasting the TAIEX based on fuzzy time series, particle swarm optimization techniques and support vector machines

Experimental results

Conclusions

Acknowledgement

Fuzzy Sets and Systems

Information Sciences

Expert System with Applications

Information Sciences

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Physica A

Physica A

Expert Systems with Applications

Expert Systems with Applications

Information Sciences

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Expert Systems with Applications

Expert Systems with Applications

Expert Systems with Applications

Expert Systems with Applications