Application of Fuzzy Time Series Model to Forecast Indonesia Stock Exchange (IDX) Composite

Transcription

1 Application of Fuzzy Time Series Model to Forecast Indonesia Stock Exchange (IDX) Composite Tri Wijayanti Septiarini* Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, Thailand Salang Musikasuwan Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, Thailand Abstract The aim of this research is to propose the fuzzy time series model for forecasting the Indonesia Stock Exchange (IDX) composite. The Mamdani inference method has been employed into the model by using centroid defuzzification. After the model has been implemented and tested, the MAPE and MSE were used to evaluate the performance of the fuzzy model. The result showed that the fuzzy time series model is a good tool for forecasting with the value of MAPE for training and testing data are 3.12% and 1.48%, respectively. Finally, it can be recommended that to improve the performance of the model, the optimization technique should be employed into the proposed model. Keywords: forecasting model, fuzzy time series, IDX composite. 1. Introduction Indonesia Stock Exchange (IDX) Composite is an index of all stock listed on the Indonesia Stock Exchange. Indonesia Stock Exchange is a stock exchange based in Jakarta, Indonesia. It was previously known as Jakarta Stock Exchange (JSX) and its name changed in 2007 after merging with Surabaya Stock Exchange (SSX). Indonesia Investments' Stock Market Update section contains a daily analysis regarding the performance of the Indonesia Stock Exchange. Indonesia Stock Exchange (IDX) is highly affected by foreign investor that can threat the economy. Domestic investor tends to invest in risk-free asset such as deposit in the bank since they are not familiar with the stock market and anxious about the risk (risk-averse type of investor). Therefore, it is important to educate domestic investor to involve in the stock exchange. Indonesia Stock Exchange is highly affected by foreign investor due to the small number of domestic investor. In 2009, it is approximately 300,000 investors (only about 0.1% from total population) which is fewer than other Asian countries such as Singapore (about1.26 million people or 30% from total population), and Malaysia (about 3 million people or 12.8% from total population). The prediction is an approximate (measurement) process about the amount of something in the future based on past data that be analyzed scientifically, especially using statistical methods. The prediction is important in financial field. The investor can use prediction result to decide policy in the future. After the data predicted is obtained, everyone who has interest in this case, can take action to reduce significant losses. For example, the multi-national company can be determined short-term financing decisions, short-term investment decisions, capital budgeting decisions, long-term financing decisions and judgments that all decisions profit is influenced by changes in currency exchange rates. In order to stabilize the economy and the IDX is not highly affected by foreign investors, Indonesia has to escalate the number of its domestic investors by educating them. For all this time, domestic investors in Indonesia are risk-averse investors. Analyze data used mathematical model is one way to educate domestic investors. The using of appropriate methods to predict have several influence factors, that are time, the pattern of data, the relationship between the previous data and the accuracy of prediction.this research proposed a fuzzy time series model to forecast Indonesia Stock Exchange

2 (IDX) composite in order to make market participants are easier to decide for do all economic activity and the accuracy of fuzzy time series model in predicting IDX composite will be evaluated. Fuzzy time series method is a dynamic process that used linguistic values as observations. This method has been proposed by proposed by Song, Q., &Chissom, B.S. (1993) to predict the number of enrollment in a university. Chen (1996) developed Song method which is further developed by Yu (2005). Again, Song method is developed by Lee, M.H. &Suhartono (2012) talking about the seasonal data and Suhartono, &Lee, M.H. (2011) proposed forecasting seasonal method and trend data. A yun et al. (2015) applied weighted fuzzy time series to forecast Trans Jogja s passengers. Rubio, A. et al. (2016) proposed forecasting portfolio return using weighted fuzzy time series methods. And Septiarini, T.W. et al. (2016) applied wavelet fuzzy model to forecast the exchange rate IDR of USD. The data that used in this research is daily data of IDX composite. 2. Fuzzy Time Series Fuzzy time series is the development of fuzzy system using time series data. The basic step of forecasting process in fuzzy time series are the following: 1. Define the universal set 2. Define fuzzy set 3. Determine the membership function of fuzzy set 4. Determine the relation of fuzzy 5. Defuzzification and forecasting Let us briefy review some prelimenry definitions. Definition 2.1 Zadeh (1965) Let } the universe of discourse. A fuzzy set A of the universe of discourse can be defined by its membership function, [ ] being the degree of membership of the element in the fuzzy set Definition 2.2 Song, Q., &Chissom, B.S. (1993) Let be a subset of real number, for being the universe of discourse in which the fuzzy sets defined, Let be a collection of fuzzy sets, then is called fuzzy time series on. Definition 2.3 Chen (1996) Let be a fuzzy time series. If for any time, and only has finite elements, then is called a time-invariant fuzzy time series. Otherwise, it is called a time-invariant fuzzy time series. According to Definition 2.3, the data on this research have to stationary data. Definition 2.4 Song, Q., &Chissom, B.S. (1993) Let and, for and. The relationship between two consecutive observations, and, is denoted by or by, where is called the left-hand side and the right hand side of the fuzzy logical relationship (FLR) 3. The forecasting of IDX with Fuzzy Time Series The processes for forecasting IDX using fuzzy time series are given as follows : Step 1. Determine stationary data The data used in this research is obtained from « in the period of December, 7 th 2015 to September, 21 st The number of data is 200 daily data. The data will be divided into 150 training data and 50 testing data. The data that use for forecasting have to be stationary. In order to obtain stationary data, the data will be differentiated. The plot of all original IDX data is shown in

3 Fig. 3.1., while Fig show the plot of the diferentiation for IDX data which used in fuzzy time series model. Fig 3.1. The plot of IDX data Fig 3.2. The plot of IDX data after being differentiated Step 2. Define the universal set of discourse U Based on stationary data, the data is obtained with the smallest and the largest in the range of and 1.029, respectively. So, the universal of discourse is U=[ , ]. Step 3. Determine the membership function of fuzzy set This model uses triangular membership function for input and output.

4 Fig 3.3. Triangular membership function of input and output From Fig 3.3., we can see that there are 7 fuzzy sets, such are A1, A2, A3, A4, A5, A6, and A7. They all have the same length. This method is refered from Chen (1996) Fuzzy Time Series method. Step 4. Determine the relation of fuzzy logic (rules) The relation of fuzzy logic is establish by training data and conducted based on fuzzy logic, or by, this refered from Definition 2.4. In this research, there are 17 rules that had been elimininated in similar case as shown in Table 4.1 Step 5. Defuzzification and forecasting Table 4.1 Fuzzy Rules No 1 A1 A5 2 A1 A6 3 A3 A5 4 A3 A6 5 A4 A3 6 A4 A4 7 A4 A5 8 A4 A6 9 A5 A1 10 A5 A3 11 A5 A4 12 A5 A5 13 A5 A6 14 A6 A1 15 A6 A4 16 A6 A5 17 A6 A6 We apply defuzzfication process using Matlab R2013a. After we obtained the result of defuzzification of stationary data, the result have to converse to the original data form for forecasting result of IDX. We can compare the value of original and forecasting data. 4. Results Once the fuzzy time series model has been implemented, the performance of the model has been evaluated with both training and testing data of IDX composite. Table 4.1 shows the value of

5 predicting comparing with real value of the testing data. We can compare the value of original and forecasting data in plot time series, as shown in Fig and Fig Table 4.1 The forecasting result of testing data No Original Data Forecasting Data No Original Data Forecasting Data

6 Fig4.1 The plot of original training data and forecasting result Fig 4.2 The plot of original testing data and forecasting result In Table 4.2, the comparison value of MAPE and MSE for training and testing data that is used to analyze fitted fuzzy time series in IDX composite. It is shown that MAPE and MSE on the testing data (1.48%, ) is lower than in the trainging data (3.12%, ). Table 4.2 The value of MAPE and MSE Training Data Testing Data MAPE MSE MAPE MSE 3.12% %

7 5. Conclusions By using fuzzy time series model to predict the short term value of IDX, the predicting result obtained a level of accuracy MAPE of 3.12% for training data and 1.48%for testing data. It means that the forecasting model is acceptable to forecast the future. Fuzzy time series is a good forecast model since the value of MAPE is less than 5%. The result of the forecasting model in this research is based on the data time series of the IDX composite only. To improve the accuracy of prediction, then further research would consider the other factors that influence the IDX composite such as the changes in a country's financial policy, interest rates, political changes in the country, and the others unpredictable factors. Finally, it can be suggested that by employing the optimization techniques can also improve the performance of the model. References A yun, Kurrotul, Abadi, A.M., &Saptaningtyas, F.Y. (2015). Application of weighted fuzzy time series model to forecast Trans Jogja s passengers. International Journal of Applied Physics and Mathematics, 5(2), Chen, S.M. (1996). Forecasting enrollments based on fuzzy time series. Fuzzy Sets and Systems, 81(3), Lee, M.H. &Suhartono. (2012). A weighted fuzzy time series for forecasting seasonal data. Journal of Quality Measurement and Analysis, 8(1), Rubio, A., Bermudez, J.D., &Vercher, E. (2016). Forecasting portfolio return using weighted fuzzy time series methods. International Journal of Approximate Reasoning, 75, Septiarini, T.W., Abadi, A.M., &Taufik, M.R. (2016). Application of wavelet fuzzy model to forecast the exchange rate IDR of USD. International Journal of Modeling and Optimization, 6(1), Suhartono, &Lee, M.H. (2011). A hybrid approach based on winter s model and weighted fuzzy time series for forecasting trend and seasonal data.journal of Mathematics and Statistics, 7(3), Song, Q., &Chissom, B.S. (1993). Forecasting enrollment with fuzzy time series-part I. Fuzzy Sets System, 54, 1-9. Yu, H.K. (2005). Weighted fuzzy time series models for TAEIX forecasting. Phisica A: Statistical Mechanics and Its Applications, 349(3-4), Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3),