Forecasting The Volatility of Bist 100 Index Return with Linear and Nonlinear Time Series Models

Öz

The successful modeling and forecasting of volatility, which is the most important element of risk indicators, minimizes financial uncertainties. Classical volatility models are insufficient to forecast structural changes in economic variables. In fact, with the recent increase in the number of artificial neural network studies, hybrid models with the combined advantages of multiple model structures have gained importance. The aim of this study is to demonstrate that hybrid models are more reliable and consistent models in forecasting volatility in variables. For this purpose, the return volatility of the Borsa Istanbul 100 index was modeled, and forecasting performance results were compared with hybrid models. According to the findings, the best forecasting performance was achieved with hybrid structures containing the exponential GARCH-Artificial Neural Networks (MSEGARCH-ANN) combination. It can be said that hybrid models are superior in the risk analysis of volatile financial instruments and in the estimation of macroeconomic variables in general.

Anahtar Kelimeler

• Volatility
• Artificial Neural Networks with Hybrid Models
• BIST 100 Index Return

Forecasting The Volatility of Bist 100 Index Return with Linear and Nonlinear Time Series Models

Öz

Risk göstergelerinin en önemli unsuru olan volatilitenin başarılı bir şekilde modellenmesi ve öngörülmesi finansal belirsizlikleri en aza indirmektedir. Klasik volatilite modelleri ekonomik değişkenlerdeki yapısal değişimleri öngörmede yetersiz kalmaktadır. Nitekim son yıllarda yapay sinir ağı çalışmalarının artmasıyla birlikte çoklu model yapılarının avantajlarını bir arada bulunduran hibrit modeller önem kazanmıştır. Bu çalışmanın amacı hibrit modellerin değişkenlerdeki volatiliteyi öngörmede daha güvenilir ve tutarlı modeller olduğunu ortaya koymaktır. Bu amaçla Borsa İstanbul 100 endeksinin getiri volatilitesi modellenmiş ve öngörü performans sonuçları hibrit modellerle karşılaştırılmıştır. Bulgulara göre en iyi öngörü performansı üstel GARCH-Yapay Sinir Ağları (MSEGARCH-ANN) kombinasyonunu içeren hibrit yapılarla elde edilmiştir. Hibrit modellerin volatil finansal araçların risk analizinde ve genel olarak makroekonomik değişkenlerin tahmininde üstün olduğu söylenebilir.

Anahtar Kelimeler

• Volatilite
• Yapay Sinir Ağları ve Hibrit Modeller
• BIST 100 Endeks Getirisi

Kaynakça

1. Abounoori, E., Elmi, Z., and Nademi, Y. (2016). Forecasting Tehran stock exchange volatility; Markov switching GARCH approach. Physica A: Statistical Mechanics and its Applications, 445, 264–282. https://doi.org/10.1016/j.physa.2015.10.024
2. Altındiş, N. (2005). ARIMA and ARCH Models in Time Series – Application to Interest Rate and Net International Reserve Series, (Master's Thesis), T.C. Marmara University, Institute of Social Sciences.
3. Augustyniak, M. (2014). Maximum likelihood estimation of the Markov-switching GARCH model. Computational Statistics and Data Analysis, 76, 61–75. https://doi.org/10.1016/j.csda.2013.01.026
4. Bildirici, M., and Ersin, Ö. (2014). Modeling Markov switching ARMA-GARCH neural networks models and an application to forecasting stock returns. The Scientific World Journal, 1–21. https://doi.org/10.1155/2014/497941
5. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
6. Cai, J. (1994). A Markov model of switching-regime ARCH, Journal of Business and Economic Statistics, 12, 309-316. https://doi.org/10.2307/1392087
7. Cappello, C., Congedi, A., De Iaco, S. and Mariella, L. (2025). Traditional prediction techniques and machine learning approaches for financial time series analysis. Mathematics, 13(3), 537. https://doi.org/10.3390/math13030537
8. Çavdar, Ş. Ç. and Aydın, A. D. (2017). The Effect of Volatility In The Borsa Istanbul Corporate Governance Index (Xkury): An Examination With The Arch, Garch And Swarch Models. Süleyman Demirel University Journal of Faculty of Economics and Administrative Sciences, 22(3).697-711. https://dergipark.org.tr/tr/download/article-file/1005522

9. Ding, Z., Granger, C.W.J. and Engle, R.F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1, 83–106. https://doi.org/10.1016/0927-5398(93)90006-D
10. Engle, R.F. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation, Econometrica 50, 987-1008. https://doi.org/10.2307/1912773
11. Gray, S. F. (1996). Modeling the conditional distribution of interest rates as a regime-switching process, Journal of Financial Economics. 42(1), 27–62. https://doi.org/10.1016/0304-405X(96)00875-6
12. Greene, W. H. (1993). Econometric Analysis. London: Prentice-Hall hc. ,https://www.ctanujit.org/uploads/2/5/3/9/25393293/_econometric_analysis_by_greence.pdf
13. Güreşen, E. and Kayakutlu, G. (2008). Forecasting stock exchange movements using artificial neural network models and hybrid models. Paper presented at the International Conference on Intelligent Information Processing. https://doi.org/10.1007/978-0-387-87685-6_17
14. Hamilton, J. D. (1989). A new approach of the economic analysis of nonstationary time series and the business cycle, Econometrica, 57, 357—384. https://doi.org/10.2307/1912559
15. Hamilton, J. D. and Susmel. R. (1994). Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics, 64:1–2, 307–333. https://doi.org/10.1016/0304-4076(94)90067-1
16. He, K., Yang, Q., Ji, L., Pan, J. and Zou, Y. (2023). Financial time series forecasting with the deep learning ensemble model. Mathematics, 11 (4). https://doi.org/10.3390/math11041054
17. Hu, L., and Shin, Y. (2008). Optimal test for Markov switching GARCH models. Studies in Nonlinear Dynamics & Econometrics, 12(3). 1-27. https://doi.org/10.2202/1558-3708.1528
18. Hull, J. C. (2006). Options, futures, and other derivatives. Pearson Education, India. https://cms.dm.uba.ar/Members/maurette/ACF2022/John_C_Hull-Options%2C_Futures_and_Other_Derivatives_7th_edition-Prentice_Hall%282008%29.pdf
19. Inclan, C. and G. C. Tiao. (1994). Use of cumulative sum of squares for retrospective detection of change of variance, Journal of the American Statistical Association. 89, 913–923. https://doi.org/10.2307/2290916
20. Işığıçok, E. (1999). Estimation of inflation variance in Turkey using ARCH and GARCH models. Uludağ University Journal of Faculty of Economics and Administrative Sciences, 17 (2), 1-17.
21. Kula, V. and Baykut, E. (2017). Analysis of the relationship between BIST Corporate Governance Index (xkury) and the Fear Index (Chicago board options exchange volatility index-VIX) . Afyon Kocatepe University Journal of Faculty of Economics and Administrative Sciences, 19(2), 27- 37. https://dergipark.org.tr/tr/pub/akuiibfd/issue/33632/373106
22. Kaya, A. and Yarbaşı, İ.Y. (2021). Forecasting of volatility in stock exchange markets by MS-GARCH approach: An application of Borsa Istanbul. Journal of Research in Economics Politics and Finance, 6(1): 16-35. https://doi.org/10.30784/epfad.740815
23. Kontopoulou VI, Panagopoulos, A.D. and Kakkos, I. (2023) A review of Arima vs. machine learning approaches for time series forecasting in data driven networks. Future Internet 15(8):255. https://doi.org/10.3390/fi15080255
24. Korkpoe, C. H. and Howard, N. (2019). Volatility model choice for Sub-Saharan frontier equity markets a Markov Regime Switching Bayesian approach. EMAJ: Emerging Markets Journal, 9(1), 69-79. https://doi.org/10.5195/emaj.2019.172
25. Kutlu, M. and Karakaya, A. (2019). Borsa Istanbul Tourism Index Volatility: Markov Regime Switching Arch Model. Journal of Yaşar University, 14,18-24. https://dergipark.org.tr/tr/pub/jyasar/issue/44178/520897
26. Marcucci J. (2005). Forecasting stock market volatility with regime-switching GARCH models. Studies in Nonlinear Dynamics and Econometrics, 9,1-42. https://doi.org/ 10.2202/1558-3708.1145
27. Mcculloch, W.S. and Pitts, W.H. (1943). A Logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysis, 5, 115-133. https://doi.org/10.1007/BF02478259
28. Lahmiri, S. and Boukadoum, M. (2015). An ensemble system based on hybrid EGARCH-ANN with different distributional assumptions to predict S&P 500 intraday volatility. Fluctuation and Noise Letters, 14(01), 1550001. https://doi.org/10.1142/S0219477515500017
29. Lamoureux, C.G. and Lastrapes, W.D. (1990). Heteroskedasticity in stock return data: volume versus GARCH effects. Journal of Finance, 45, 221–229. https://doi.org/10.1111/j.1540-6261.1990.tb05088.x
30. Nelson, D.B. (1990). Stationarity and persistence in the GARCH(1, 1) model. Econometric Theory 6, 318-334. https://www.jstor.org/stable/3532198
31. Nelson, D.B. (1991). Conditional heteroskedasticity in asset returns: a new approach. Econometrica, 59, 347-370. https://doi.org/10.2307/2938260
32. Özden, Ü.H. (2008). Analysis of BIST 100 composite index return volatility, İstanbul Ticaret University Journal of Socail Sciences, 13, 339-350. https://www.ticaret.edu.tr/uploads/yayin/dergi/s13/339-350.pdf
33. Roh, T. H. (2007). Forecasting the volatility of stock price index. Expert Systems with Applications, 33, 916–922. https://doi.org/10.1016/j.eswa.2006.08.001
34. Sevüktekin, M. and Çınar, M. (2006). Modeling and Forecasting of Istanbul Stock Exchange Return Volatility, Ankara University Journal of Faculty of Socail Sciences, 61 (4), 243-265. https://dergipark.org.tr/tr/pub/ausbf/issue/3215/44765
35. Schwert, G. W. (1990). Stock volatility and the crash of 87, Review of Financial Studies, 3, 77-102. https://www.jstor.org/stable/2961958
36. Tan, C. Y., Koh, Y. B., Ng, K. H. ve Ng, K. H. (2021). Dynamic volatility modelling of Bitcoin using time-varying transition probability Markov-switching GARCH model. The North American Journal of Economics and Finance, 56, 101377. https://doi.org/10.1016/j.najef.2021.101377
37. Taylor, S. (1986). Modelling Financial Time Series. Wiley, New York.
38. Zakoian, J.M. (1994). Threshold heteroskedasticity models. Journal of Economic Dynamics and Control, 15:931-955. https://doi.org/10.1016/0165-1889(94)90039-6