Comparison of Fuzzy Grey Markov Model (1,1) and Fuzzy Grey Markov Model (2,1) in Forecasting Gold Prices in Indonesia

Arthamevia Najwa Soraya, Firdaniza Firdaniza, Kankan Parmikanti

Abstract


Currently, gold investment is considered promising despite the ever-changing price of gold. However, obtaining optimal profits is a challenge for investors. Therefore, a proper forecasting method is needed to forecast the gold price so investors can know the best transaction time. This study used two forecasting methods: the Fuzzy Grey Markov Model (1,1) and a new, never-before-used approach, the Fuzzy Grey Markov Model (2,1). The Fuzzy Grey Markov Model (2,1) approach is interesting because it can be considered for forecast data that shows varying increases and decreases, such as the gold price data used in this study. Both methods are combined models that utilize fuzzy logic to handle uncertainty in data; the Grey model forms a forecasting model, and the Markov chain determines the state transition probability matrix. Next, the error rates of the two methods are compared based on the Mean Absolute Percentage Error (MAPE) value to obtain the best forecasting method. As a result of this study, the Fuzzy Grey Markov Model (1,1) was chosen as the best forecasting method with a MAPE value of 0.28%.

Keywords


Forecasting; Gold Price; Fuzzy Grey Markov Model (1,1); Fuzzy Grey Markov Model (2,1)

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References


J. Nazarudin, N. Gusriani, K. Parmikanti, and S. Susanti, “Article Application of Threshold Generalized Autoregressive Conditional Heteroscedastic (TGARCH) Model in Forecasting the LQ45 Stock Price Return,” Eksakta : Berkala Ilmiah Bidang MIPA, vol. 24, no. 2, pp. 271–284, 2023, doi: 10.24036/eksakta/vol24-iss02/369.

A. Manickam, S. Indrakala, and P. Kumar, “A Novel Mathematical Study on the Predictions of Volatile Price of Gold Using Grey Models,” Contemporary Mathematics (Singapore), vol. 4, no. 2, pp. 270–285, 2023, doi: 10.37256/cm.4220232389.

R. Gupta, C. Pierdzioch, and W.-K. Wong, “A Note on Forecasting the Historical Realized Variance of Oil-Price Movements: The Role of Gold-to-Silver and Gold-to-Platinum Price Ratios,” Energies (Basel), vol. 14, no. 20, p. 6775, 2021, doi: 10.3390/en14206775.

T. Andriyanto, “Sistem Peramalan Harga Emas Antam Menggunakan Double Exponential Smoothing,” Intensif, vol. 1, no. 1, p. 1, 2017, doi: 10.29407/intensif.v1i1.531.

S. Yurinanda, C. Multahadah, and R. Aryani, “Development of COVID-19 Case in District and City of Jambi Province with Exponential Smoothing Methode,” Eksakta : Berkala Ilmiah Bidang MIPA, vol. 21, no. 2, pp. 110–123, 2020, doi: 10.24036//eksakta/vol21-iss2/244.

M. Yanto, S. Sanjaya, Yulasmi, D. Guswandi, and S. Arlis, “Implementation multiple linear regresion in neural network predict gold price,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 22, no. 3, pp. 1635–1642, 2021, doi: 10.11591/ijeecs.v22.i3.pp1635-1642.

X. Li, D. Li, X. Zhang, G. Wei, L. Bai, and Y. Wei, “Forecasting regular and extreme gold price volatility: The roles of asymmetry, extreme event, and jump,” J Forecast, vol. 40, no. 8, pp. 1501–1523, 2021, doi: 10.1002/for.2781.

D. Makala and Z. Li, “Prediction of gold price with ARIMA and SVM,” J Phys Conf Ser, vol. 1767, no. 1, p. 012022, 2021, doi: 10.1088/1742-6596/1767/1/012022.

D. Ju-Long, “Control problems of grey systems,” Syst Control Lett, vol. 1, no. 5, pp. 288–294, 1982, doi: 10.1016/S0167-6911(82)80025-X.

Y. H. Feng, X. Kong, L. Wang, Y. Zhang, J.Y. Zhang, P. D. Yuan, and Y. N. Li, “Prediction of Motorcycle Seat Styling Based on Grey Modelling (1,1).” Computer-Aided Design & Applications, vol. 16, no. 5, pp. 789-802, 2019, doi: 10.14733/cadaps.2019.789-802.

B. Zeng, X. Ma, and J. Shi, “Modeling Method of the Grey GM(1,1) Model with Interval Grey Action Quantity and Its Application,” Complexity, pp. 1–10, 2019, doi: 10.5772/intechopen.83801.

J. Lin, K. Zhu, Z. Liu, J. Lieu, and X. Tan, “Study on a simple model to forecast the electricity demand under China’s new normal situation,” Energies, vol. 12, no. 11: 2220, 2019, doi: 10.3390/en12112220.

Y. Yang, C. Ming, and Q. Liu, “Research on Forecasting the Number of Tourists in Anyang Based on Grey System GM (1, 1),” Scholars Journal of Physics, Mathematics and Statistics, vol. 7, pp. 76-81, 2020, doi: 10.36347/sjpms.2020.v07i06.001.

T. Škrinjarić and M. Čimešija, “Selected Applications of Grey Models in Stock Price Prediction,” Recent Applications of Financial Risk Modelling and Portfolio Management, pp. 346-326, 2021, doi: 10.4018/978-1-7998-5083-0.ch017.

Z. Q. Jia, Z. F. Zhou, H. J. Zhang, B. Li, and Y. X. Zhang, “Forecast of coal consumption in Gansu Province based on Grey-Markov chain model,” Energy, vo. 199, 2020, doi: 10.1016/j.energy.2020.117444.

P. S. Kumar, and D. Thamaraiselvi, “Prediction Of Estro-Progestin Supplimentation Enhances Growth Hormone Secretion In Postmenopausal Women By Using GM(2,1) And Grey-Markov(2,1) Model,” Journal of Xidian University, vol. 14, no. 4, pp. 803-810, 2020, doi: 10.37896/jxu14.4/098.

L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965, doi: 10.1016/S0019-9958(65)90241-X.

N. Geng, Y. Zhang, Y. Sun, Y. Jiang, and D. Chen, “Forecasting China’s Annual Biofuel Production Using an Improved Grey Model,” Energies (Basel), vol. 8, no. 10, pp. 12080–12099, 2015, doi: 10.3390/en81012080.

K. Govindan, S. Ramalingam, and S. Broumi, “Traffic volume prediction using intuitionistic fuzzy Grey-Markov model,” Neural Comput Appl, vol. 33, no. 19, pp. 12905–12920, 2021, doi: 10.1007/s00521-021-05940-9.

D. Nagarajan, R. Sujatha, G. Kuppuswami, and J. Kavikumar, “Real-time forecasting of the COVID 19 using fuzzy grey Markov: a different approach in decision-making,” Computational and Applied Mathematics, vol. 41, no. 6, p. 248, 2022, doi: 10.1007/s40314-022-01949-5.

S. Liu and Y. Lin, Grey information : theory and practical applications. London: Springer-Verlag, 2006.

R.-C. Tsaur, “A fuzzy time series-markov chain model with an application to forecast the exchange rate between the taiwan and us dollar,” International Journal of Innovative Computing, Information and Control, vol. 8, no. 7, pp. 4931–4942, 2012. [Online]. Available at: http://www.ijicic.org/ijicic-11-04029.pdf.

S. Kusumadewi and H. Purnomo, Aplikasi Logika Fuzzy : untuk Pendukung Keputusan, 2nd ed. Yogyakarta: Graha Ilmu, 2020.

S. Osaki, Applied Stochastic System Modeling. Japan: Springer, 1992.

L.-X. Wang, A Course in Fuzzy Systems and Control. New Jearsy: Prentice Hall,1997.

D. Jain, S. Sharma, and P. Dhiman, “Comparative Analysis of Defuzzification Techniques for Fuzzy Output,” J Algebr Stat, vol. 13, no. 2, pp. 874–882, 2022, doi: 10.52783/jas.v13i2.234.

K. D. Lawrence, R. K. Klimberg, and S. M. Lawrence, Fundamentals of forecasting using Excel. Industrial Press, 2009.




DOI: https://doi.org/10.37905/jjom.v6i2.26679



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