Garch Ve Yapay Sinir Ağları Modelleri Yardımıyla Volatilite Tahmini: Türk Borsası Örneği

Year 2023, Volume: 25 Issue: 2, 572 - 595, 31.12.2023

Cumhur Şahin

Abstract

Küreselleşme olgusunun 1990’lı yıllarla birlikte baskın hale gelmesiyle birlikte uluslararası ekonomik düzende ülkelerin birbiriyle etkileşim ve entegrasyonunun çarpıcı bir biçimde artması ve iktisadi bağların kuvvetlenmesi, finansal piyasalarda yaşanan hızlı değişimler, pazarlar arasındaki ilişkilerin ve risklerin artmasına yol açmaktadır. Finansal piyasalar hali hazırda ortaya çıkan gelişmelere karşı çok daha hassas hale gelmektedir. Finansla ilgili akademik araştırmalarda özellikle finansal zaman serileri ve bunların öngörüsüne yönelik çalışmalar oldukça önemli bir yer tutmaktadır. Dalgalanma veya oynaklık olarak da ifade edilebilen volatilite kavramı finansal piyasalarda vazgeçilmez bir yere sahiptir. Bundan dolayı, volatilitenin en yüksek duyarlılıkla tahmin edilmesi son derece yararlıdır. Son yıllarda finansal endekslerin oynaklığını tahmin etmek için GARCH (Generalized Autoregressive Conditional Heteroskedasticity-Genelleştirilmiş Otoregresif Koşullu Değişen Varyans) tipi modellerin yanı sıra ANN (Artificial Neural Network-yapay sinir ağları) modelleri de yaygın olarak kullanılmaktadır. Bu araştırmanın amacı, farklı model türlerinin birleştirilmesinin menkul kıymet borsa endeks volatilitesi tahminlerini iyileştirip iyileştiremeyeceğine karar verilmesidir. Bu nedenle, BIST-100 Endeksi volatilitesini tahmin etme yetenekleri açısından iki hibrit model kullanılarak, Asimetrik GARCH modeli ve bir yapay sinir ağı modeli karşılaştırılmıştır. Sonuçlar, bir EGARCH modeli tarafından elde edilen şartlı volatilite tahminlerinin yanı sıra, getirileri ve tarihsel değerleri girdi olarak kabul eden bir yapay sinir ağına dayanan hibrit modelin en iyi tahmin gücünü sağladığını ortaya koymaktadır. Ayrıca, bu hibrit modelin baskınlığı, tahminin geri kalan modelleri de kapsayacak şekilde olmasıdır. Son olarak, Türk borsasında önemli kaldıraç etkileri bulunduğu gösterilmiştir.

Keywords

Yapay Sinir Ağı, GARCH Modelleri, Volatilite Tahmini

References

• Abounoori, A. A., Naderi, E., Alikhani, N. G. & Amiri, A. (2013). Financial Time Series Forecasting by Developing a Hybrid Intelligent System, MPRA Paper 45615. Germany: University Library of Munich.
• Ahmed, A. E. M. & Suliman, S. Z. (2011). Modeling Stock Market Volatility Using GARCH Models Evidence from Sudan. International Journal of Business and Social Science, 2(23), 114-128.
• Awartani, B. M. & Corradi, V. (2005). Predicting the Volatility of the S&P500 Stock Index Via GARCH Models: The Role of Asymmetries. International Journal of Forecasting, 21(1), 167-183.
• Bhattacharya, S. & Ahmed, A. (2018). Forecasting Crude Oil Price Volatility in India Using a Hybrid ANN-GARCH Model. International Journal of Business Forecasting and Marketing Intelligence, 4(4), 446-457.
• Bildirici, M. & Ersin, Ö. Ö. (2009). Improving Forecasts of GARCH Family Models with the Artificial Neural Networks: An Application to the Daily Returns in Istanbul Stock Exchange. Expert Systems with Applications, 36(4), 7355-7362.
• Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307-327.
• Box, G. E. & Jenkins, G. M. (1976). Time Series Analysis, Control, and Forecasting. San Francisco, CA: Holden Day.
• Brooks, C. (2008). Introductory Econometrics for Finance. 2nd ed. Cambridge, England: Cambridge University Press.
• Chong, Y. Y. & Hendry, D. F. (1986). Econometric Evaluation of Linear Macro-Economic Models. Review of Economic Studies, 53(4): 671-690.
• Cook, S. (2012). An Historical Perspective on the Forecasting Performance of the Treasury Model: Forecasting the Growth in UK Consumers’ Expenditure. Applied Economics, 44(5), 555-563.
• Curto, J. D., Pinto, J. C. & Tavares, G. N. (2009). Modeling Stock Markets’ Volatility Using GARCH Models with Normal, Student’s T And Stable Paretian Distributions. Statistical Papers, 50(2), 311-321.
• Çam, S., Ballı, E. & Sigeze, Ç. (2017). Petrol Fiyatlarındaki Oynaklığın ARCH/GARCH Modelleri ve Yapay Sinir Ağları Algoritması ile Tahmini. Uluslararası Yönetim, İktisat ve İşletme Dergisi, (ICMEB 17 Özel Sayısı), 588-597.
• Day, T. E. & Lewis, C. M. (1992). Stock Market Volatility and the Information Content of Stock Index Options. Journal of Econometrics, 52(1-2), 267-287.
• De Clerk, L. & Savelev, S. (2022). AI Algorithms for Fitting GARCH Parameters to Empirical Financial Data. Physica A: Statistical Mechanics and its Applications, 603, 127869.
• Dhamija, A. K. & Bhalla, V. K. (2010). Financial Time Series Forecasting: Comparison of Neural Networks and ARCH Models. International Research Journal of Finance and Economics, 49, 185-202.
• Dickey, D. A. & Fuller, W. A. (1979). Distribution of the Estimators for Autoregressive Time series with a Unit Root. Journal of the American Statistical Association, 74(366a), 427-431.
• Dickey, D. A. & Fuller, W. A. (1981). Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica: Journal of the Econometric Society, 49(4), 1057-1072.
• Donaldson, R. G. & Kamstra, M. (1997). An Artificial Neural Network GARCH Model for International Stock Return Volatility. Journal of Empirical Finance, 4(1), 17-46.
• Dritsakis, C. (2017). An Empirical Evaluation in GARCH Volatility Modeling: Evidence from the Stockholm Stock Exchange. Journal of Mathematical Finance, 7(02), 366-390.
• Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica: Journal of the Econometric Society, 50(4), 987-1007.
• Engle, R. F. & Patton, A. J. (2007). What Good Is a Volatility Model? In: Forecasting Volatility in the Financial Markets. Netherlands: Elsevier. 47-63.
• Fahimifard, S. M., Homayounifar, M., Sabouhi, M. & Moghaddamnia, A. R. (2009). Comparison of ANFIS, ANN, GARCH and ARIMA Techniques to Exchange Rate Forecasting. Journal of Applied Sciences, 9(20), 3641-3651.
• Fair, R. C. & Shiller, R. J. (1989). The Informational Content of Ex Ante Forecasts. The Review of Economics and Statistics, 71(2), 325-331.
• Franses, P. H. & Van Dijk, D. (1996). Forecasting Stock Market Volatility Using (Non-linear) GARCH Models. Journal of Forecasting, 15(3), 229-235.
• Georgescu, V. & Dinucă, E. C. (2011). Evidence of Improvement in Neural Network Based Predictability of Stock Market Indexes Through Co-Movement Entries. In: Recent Advances in Applied and Biomedical Informatics and Computational Engineering in Systems Applications. 11th WSEAS International Conference on Applied Informatics and Communications, Florence, Italy 2011, 412-417.
• Ghiassi, M. D. K., Zimbra, D. K. & Saidane, H. (2006). Medium Term System Load Forecasting with a Dynamic Artificial Neural Network Model. Electric Power Systems Research, 76(5), 302-316.
• Glosten, L. R., Jagannathan, R. & Runkle, D.E. (1993). On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, 48(5), 1779-1801.
• Güreşen, E., Kayakutlu, G. & Daim, T. U. (2011). Using Artificial Neural Network Models in Stock Market Index Prediction. Expert Systems with Applications, 38(8), 10389-10397.
• Hajizadeh, E., Seifi, A., Zarandi, M. F. & Turksen, I. B. (2012). A Hybrid Modeling Approach for Forecasting the Volatility of S&P 500 Index Return. Expert Systems with Applications, 39(1), 431-436.
• Heston, S. L. (1993). A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. The Review of Financial Studies, 6(2), 327-343.
• Jarque, C. M. & Bera, A. K. (1980). Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals. Economics Letters, 6(3), 255-259.
• Khan, A. U. & Gour, B. (2013). Stock Market Trends Prediction Using Neural Network Based Hybrid Model. International Journal of Computer Science Engineering and Information Technology Research, 3(1), 11-18.
• Ko, P. C. (2009). Option Valuation Based on the Neural Regression Model. Expert Systems with Applications, 36(1), 464-471.
• Koopman, S. J., Jungbacker, B. & Hol, E. (2005). Forecasting Daily Variability of the S&P 100 Stock Index Using Historical, Realised and Implied Volatility Measurements. Journal of Empirical Finance, 12(3), 445-475.
• Kristjanpoller, W., Fadic, A. & Minutolo, M. C. (2014). Volatility Forecast Using Hybrid Neural Network Models. Expert Systems with Applications, 41(5), 2437-2442.
• Kryzanowski, L., Galler, M. & Wright, D. W. (1993). Using Artificial Neural Networks to Pick Stocks. Financial Analysts Journal, 49(4), 21-27.
• Lahmiri, S. (2017). Modeling and Predicting Historical Volatility in Exchange Rate Markets. Physica A: Statistical Mechanics and its Applications, 471, 387-395.
• Lewis, N. D. (2017). Neural Networks for Time Series Forecasting with R: An Intuitive Step by Step Blueprint for Beginners. United States: Create Space Independent Publishing Platform.
• Liu, H. C. & Hung, J. C. (2010). Forecasting S&P-100 Stock Index Volatility: The Role of Volatility Asymmetry and Distributional Assumption in GARCH Models. Expert Systems with Applications, 37(7), 4928- 4934.
• Liu, W. K. & So, M. K. P. (2020). A GARCH Model with Artificial Neural Networks. Information, 11(10), 489.
• Ljung, G. M. & Box, G. E. (1978). On a Measure of Lack of Fit in Time Series Models. Biometrika, 65(2), 297-303.
• Lu, Y. K. & Perron, P. (2010). Modeling and Forecasting Stock Return Volatility Using a Random Level Shift Model. Journal of Empirical Finance, 17(1), 138-156.
• Lu, X., Que, D. & Cao, G. (2016). Volatility Forecast Based on the Hybrid Artificial Neural Network and GARCH-Type Models. Procedia Computer Science, 91, 1044-1049.
• Luo, Y. & Shah, A. (2007). A Local-Patch Based Multi-Stage Artificial Neural Network Training Procedure and Its Application to Material Characterization. International Journal of Computational Methods, 4(3), 439-458.
• Maciel, L. S. & Ballini, R. (2010). Neural Networks Applied to Stock Market Forecasting: An Empirical Analysis. Journal of the Brazilian Neural Network Society, 8(1), 3-22.
• Marcucci, J. (2005). Forecasting Stock Market Volatility with Regime-Switching GARCH Models. Studies in Nonlinear Dynamics and Econometrics, 9(4), 6-26.
• Meissner, G. & Kawano, N. (2001). Capturing the Volatility Smile of Options on High-Tech Stocks-a Combined GARCH Neural Network Approach. Journal of Economics and Finance, 25(3), 276-292.
• Merh, N., Saxena, V. P. & Pardasani, K. R. (2010). A Comparison between Hybrid Approaches of ANN and ARIMA for Indian Stock Trend Forecasting. Business Intelligence Journal, 3(2), 23-43.
• Metin, N., Karadağ, K. & Terzioğlu, M. K. (2020). MLP/RBF Ağ Mimarileriyle Hibrit MGARCH-ANN Model Performans Karşılaştırması: Petrol Fiyat Oynaklığı. Ankara Hacı Bayram Veli Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, (Özel Sayı), 78-93.
• Monfared, S. A. & Enke, D. (2014). Volatility Forecasting Using a Hybrid GJR-GARCH Neural Network Model. Precedia Computer Science, 36, 246-253.
• Nazarian, R., Alikhani, N. G., Naderi, E. & Amiri, A. (2013). Forecasting Stock Market Volatility: A Forecast Combination Approach. MPRA Paper, 46786, 1-20, Germany: University Library of Munich.
• Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica: Journal of the Econometric Society, 59(2), 347-370.
• Özbey, F. & Paksoy, S. (2020). GARCH Ailesi Modelleri ve ANN Entegrasyonu ile BİST 100 Endeks Getirisinin Volatilite Tahmini. Business and Economics Research Journal, 11(2), 385-396.
• Pagan, A. R. & Schwert, G. W. (1990). Alternative Models for Conditional Stock Volatility. Journal of Econometrics, 45(1-2), 267-290.
• Pai, P. F. & Lin, C. S. (2005). A Hybrid ARIMA and Support Vector Machines Model in Stock Price Forecasting. Omega, 33(6), 497-505.
• Pakdaman, M., Ahmadian, A., Effati, S., Salahshour, S. & Baleanu, D. (2017). Solving Differential Equations of Fractional Order Using an Optimization Technique Based on Training Artificial Neural Network. Applied Mathematics and Computation, 293, 81-95.
• Qi, M. (1999). Nonlinear Predictability of Stock Returns Using Financial and Economic Variables. Journal of Business and Economic Statistics, 17(4), 419-429.
• Qi, M. & Maddala, G. S. (1999). Economic Factors and the Stock Market: A New Perspective. Journal of Forecasting, 18(3), 151-166.
• Quah, T. S. (2007). Using Neural Network for DJIA Stock Selection. Engineering Letters, 15(1), 3-8.
• Ramos-Perez, E., Alonso-González, P. J. & Núñez-Velázquez, J. J. (2019). Forecasting Volatility with a Stacked Model Based on a Hybridized Artificial Neural Network. Expert Systems with Applications, 129, 1-9.
• Roh, T. H. (2007). Forecasting the Volatility of Stock Price Index. Expert Systems with Applications, 33(4), 916-922.
• Sahin, S., Tolun, M. R. & Hassanpour, R. (2012). Hybrid Expert Systems: A Survey of Current Approaches and Applications. Expert Systems with Applications, 39(4), 4609-4617.
• Schittenkopf, C., Dorffner, G. & Dockner, E. J. (2000). Forecasting Time‐Dependent Conditional Densities: A Semi Non‐Parametric Neural Network Approach. Journal of Forecasting, 19(4), 355-374.
• Soni, S. (2011). Applications of ANNs in Stock Market Prediction: A Survey. International Journal of Computer Science and Engineering Technology, 2(3), 71-83.
• Tseng, C. H., Cheng, S. T., Wang, Y. H. & Peng, J. T. (2008). Artificial Neural Network Model of the Hybrid EGARCH Volatility of the Taiwan Stock Index Option Prices. Physica A: Statistical Mechanics and its Applications, 387(13), 3192-3200.
• Vejendla, A. & Enke, D. (2013a). Evaluation of GARCH, RNN and FNN Models for Forecasting Volatility in the Financial Markets. IUP Journal of Financial Risk Management, 10(1), 41-49.
• Vejendla, A. & Enke, D. (2013b). Performance Evaluation of Neural Networks and GARCH Models for Forecasting Volatility and Option Strike Prices in a Bull Call Spread Strategy. Journal of Economic Policy and Research, 8(2), 1-19.
• Wang, Y. H. (2009). Nonlinear Neural Network Forecasting Model for Stock Index Option Price: Hybrid GJR-GARCH Approach. Expert Systems with Applications, 36(1), 564-570.
• Wei, W. (2002). Forecasting Stock Market Volatility with Non-Linear GARCH Models: A Case for China. Applied Economics Letters, 9(3), 163-166.
• Wei, L. Y., Chen, T. L. & Ho, T. H. (2011). A Hybrid Model Based on Adaptive-Network-Based Fuzzy Inference System to Forecast Taiwan Stock Market. Expert Systems with Applications, 38(11), 13625-13631. https://www.matriksdata.com/website/, Erişim tarihi: 19.12.2022.