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International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(1): 49-56

Published online March 25, 2021

https://doi.org/10.5391/IJFIS.2021.21.1.49

© The Korean Institute of Intelligent Systems

Fuzzy Mediation Analysis for KOSPI-Related Variables

Dae Jong Kim1, Yoo Young Koo2, and Jin Hee Yoon3

1Department of Business Administration, Sejong University, Seoul, Korea
2University College, Yonsei University, Incheon, Korea
3Department of Mathematics and Statistics, Sejong University, Seoul, Korea

Correspondence to :
Jin Hee Yoon (jin9135@sejong.ac.kr)

Received: February 22, 2021; Revised: March 14, 2021; Accepted: March 17, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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Stock prices and bond interest rates are inversely related. The current account plays the most important role in the rise of composite stock index. When the trade surplus increases, stock prices rise sharply. Conversely, when the exchange rate and government bond interest rates increase, the composite stock index decreases. The stock index is influenced by several economic variables, politics, the economy, and investment sentiment. In real situations, such financial variables are mostly fuzzy variables. For example, the Korea Composite Stock Price Index (KOSPI) is recorded based on the closing price. However, the daily KOSPI has many values, such as the open price, low price, and high price; therefore, if only the closing price is used for analysis, only partial information is. To analyze the relationship between KOSPI-related variables, the KOSPI, stock deposits, government bond interest rates, and foreign security investment data are applied. We investigated the mediated relation of variables, known as mediation analysis. In particular, we implemented fuzzy mediation analysis owing to the ambiguity of given data. In the data analysis, we proposed several fuzzy mediation models using fuzzy transformed data.

Keywords: Fuzzy numbers, Fuzzy data, KOSPI, Fuzzy mediation analysis

Conflict of Interest

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No potential conflict of interest relevant to this article was reported

Biographies

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Dae Jong Kim received his B.A. from Hankuk University of Foreign Studies, MBA in economics from Korea University, Ph.D. in economics from Sogang University, Korea. He is currently a faculty in the department of business school at Sejong University, Seoul, Korea. He is Present, Korea Institute for Business and Economics and is listed on the Marquis Who’s Who. His research interests include fuzzy regression analysis, fuzzy time series, optimization, intelligent systems, and applied economics.

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Jin Hee Yoon received her B.S., M.S., and Ph.D. degrees in mathematics from Yonsei University, Korea. She is currently a faculty member in the department of mathematics and statistics at Sejong University, Seoul, Korea. Her research interests include fuzzy regression analysis, fuzzy time series, optimization, intelligent systems, and machine learning. She is a board member of the Korean Institute of Intelligent Systems (KIIS) and has been working as an associate editor, guest editor, and editorial board member of several journals, including SCI and SCIE. In addition, she has been working as an organizer and committee member of several international conferences.

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Yoo Young Koo received her B.S., M.S., and Ph.D. degrees in Mathematics from Yonsei University, Korea. She is currently a faculty member at the University College of Yonsei University, Incheon, Korea. Her research interests include statistical analysis, data analysis, machine learning, and deep learning.

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Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(1): 49-56

Published online March 25, 2021 https://doi.org/10.5391/IJFIS.2021.21.1.49

Copyright © The Korean Institute of Intelligent Systems.

Fuzzy Mediation Analysis for KOSPI-Related Variables

Dae Jong Kim1, Yoo Young Koo2, and Jin Hee Yoon3

1Department of Business Administration, Sejong University, Seoul, Korea
2University College, Yonsei University, Incheon, Korea
3Department of Mathematics and Statistics, Sejong University, Seoul, Korea

Correspondence to:Jin Hee Yoon (jin9135@sejong.ac.kr)

Received: February 22, 2021; Revised: March 14, 2021; Accepted: March 17, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Stock prices and bond interest rates are inversely related. The current account plays the most important role in the rise of composite stock index. When the trade surplus increases, stock prices rise sharply. Conversely, when the exchange rate and government bond interest rates increase, the composite stock index decreases. The stock index is influenced by several economic variables, politics, the economy, and investment sentiment. In real situations, such financial variables are mostly fuzzy variables. For example, the Korea Composite Stock Price Index (KOSPI) is recorded based on the closing price. However, the daily KOSPI has many values, such as the open price, low price, and high price; therefore, if only the closing price is used for analysis, only partial information is. To analyze the relationship between KOSPI-related variables, the KOSPI, stock deposits, government bond interest rates, and foreign security investment data are applied. We investigated the mediated relation of variables, known as mediation analysis. In particular, we implemented fuzzy mediation analysis owing to the ambiguity of given data. In the data analysis, we proposed several fuzzy mediation models using fuzzy transformed data.

Keywords: Fuzzy numbers, Fuzzy data, KOSPI, Fuzzy mediation analysis

Fig 1.

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Figure 1.

(a–f) Various types of fuzzy numbers.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 49-56https://doi.org/10.5391/IJFIS.2021.21.1.49

Fig 2.

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Figure 2.

Simple mediation model (conceptual model).

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 49-56https://doi.org/10.5391/IJFIS.2021.21.1.49

Fig 3.

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Figure 3.

Simple mediation model (statistical model).

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 49-56https://doi.org/10.5391/IJFIS.2021.21.1.49

Fig 4.

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Figure 4.

Trend analysis of 10-year US government bonds (1980 to 2020). X-axis is time (month) and Y-axis is interest rate (%). Bond rates decline over time. (Source: Bank of Korea, http://ecos.bok.or.kr).

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 49-56https://doi.org/10.5391/IJFIS.2021.21.1.49

Fig 5.

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Figure 5.

Trends in Korea and US government bonds (2000–2020). Dashed line is 3-year Korean government bonds and solid line is 10-year US government bonds. X-axis is time (month) and Y-axis is interest rate (%). Bond rates decline over time. (Source: Bank of Korea, http://ecos.bok.or.kr).

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 49-56https://doi.org/10.5391/IJFIS.2021.21.1.49

Fig 6.

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Figure 6.

Fuzzy mediation analysis of stock deposit data.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 49-56https://doi.org/10.5391/IJFIS.2021.21.1.49

Fig 7.

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Figure 7.

Fuzzy mediation analysis of foreign security investment data.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 49-56https://doi.org/10.5391/IJFIS.2021.21.1.49

Fig 8.

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Figure 8.

Fuzzy mediation analysis of stock deposit and foreign security investment data.

The International Journal of Fuzzy Logic and Intelligent Systems 2021; 21: 49-56https://doi.org/10.5391/IJFIS.2021.21.1.49

Table 1 . Descriptive statistics.

KOSPIGovernment bond interest rateStock deposit (103$)Foreign securities investment (1012 W)
Average1614.73.5016453440342.2
Median1858.83.5914586897351.1
Standard deviation564.21.507950863157.2
Minimum value504.00.83779595265.3
Maximum value2533.56.5856066861657.7

Table 2 . Correlation coefficients.

KOSPIGovernment bond interest rateStock depositForeign securities investment
KOSPI1
Government bond interest rate−0.7421
Stock deposit0.715−0.8021
Foreign securities investment0.952−0.8350.8141

Table 3 . Effects for Stock Deposit on KOSPI.

MethodEffect
Total effectDirect effectIndirect effect
CMA−0.791−0.505−0.286
FMA−0.639−0.255−0.384

Table 4 . Effects for foreign security investment on KOSPI.

MethodEffect
Total effectDirect effectIndirect effect
CMA−0.7910.188−0.979
FMA−0.6390.009−0.648

Table 5 . Effects for stock deposit and foreign security investment on KOSPI.

MethodEffect
Total effectDirect effectIndirect effect
CMA−0.7910.1300.115, −1.036
FMA−0.6390.0010.024, −0.664

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