VOLATILITY DYNAMICS AND SPILLOVERS IN BIST SECTOR INDICES: A GARCH (1,1) AND FOURIER VARIANCE CAUSALITY APPROACH

Öz

This study investigates the dynamic structure of volatility and sectoral spilo among Borsa Istanbul sector indices using both conventional and advanced econometric methods. Utilizing daily closing data from 2018 to 2024, the analysis first applies the Generalized Autoregressive Conditional Heteroscedasticity GARCH (1,1) model to reveal the volatility characteristics of sector indices. In the subsequent stage, the Fourier causality-in-variance test is employed to examine the direction and magnitude of volatility spillovers between indices from a frequency-domain perspective. The findings indicate that volatility transmission in the Turkish market is predominantly asymmetric and directional, with shocks in the technology and financial sectors quickly propagating to the industrial and services indices, while certain sector pairs display mutual and strong interdependence. The Fourier approach demonstrates that volatility spillovers do not occur merely in specific time windows, but persist across both short-term shocks and long-term economic cycles.

Anahtar Kelimeler

• Borsa Istanbul
• Volatility
• GARCH
• Fourier causality in variance

BİST SEKTÖR ENDEKSLERİNDE VOLATİLİTE DİNAMİKLERİ VE YAYILIMI: GARCH (1,1) VE FOURİER VARYANSTA NEDENSELLİK YAKLAŞIMI

Öz

Bu çalışma, Borsa İstanbul sektör endekslerinde volatilitenin dinamik yapısını ve sektörler arası yayılımı hem geleneksel hem de modern ekonometrik yaklaşımlarla incelemektedir. Çalışmada, 2018-2024 dönemine ait günlük kapanış verileri kullanılarak, ilk aşamada Genelleştirilmiş Otoregresif Koşullu Değişen Varyans GARCH (1,1) modeli ile sektör endekslerinin volatilite yapısı ortaya konmuştur. Sonraki aşamada ise Fourier varyansta nedensellik testi ile endeksler arası volatilite aktarımının yönü ve şiddeti frekans-temelli olarak analiz edilmiştir. Elde edilen bulgular, Türkiye piyasasında volatilite aktarımının çoğunlukla asimetrik ve yönlü olduğunu, teknoloji ve mali sektörlerdeki şokların sanayi ve hizmetler endekslerine kısa sürede yayıldığını, bazı sektör çiftlerinde ise karşılıklı ve güçlü etkileşimlerin bulunduğunu göstermektedir. Fourier yaklaşımı, sektörler arası volatilite transferinin yalnızca belirli zaman aralıklarında değil hem kısa vadeli ani şoklar hem de uzun vadeli ekonomik döngüler boyunca gerçekleştiğini ortaya koymuştur.

Anahtar Kelimeler

• Borsa İstanbul
• Volatilite
• GARCH
• Fourier varyansta nedensellik

Kaynakça

1. Billio, M., Getmansky, M., Lo, A. W., & Pelizzon, L. (2012). Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics, 104(3), 535–559. https://doi.org/10.1016/j.jfineco.2011.12.010
2. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1
3. Diebold, F. X., & Yılmaz, K. (2009). Measuring financial asset return and volatility spillovers, with application to global equity markets. The Economic Journal, 119(534), 158–171. https://doi.org/10.1111/j.1468-0297.2008.02208.x
4. Diebold, F. X., & Yılmaz, K. (2012). Better to give than to receive: Predictive directional measurement of volatility spillovers. International Journal of Forecasting, 28(1), 57–66. https://doi.org/10.1016/j.ijforecast.2011.02.006
5. Diebold, F. X., & Yılmaz, K. (2014). On the network topology of variance decompositions: Measuring the connectedness of financial firms. Journal of Econometrics, 182(1), 119–134. https://doi.org/10.1016/j.jeconom.2014.04.012
6. Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49(4), 1057–1072. https://doi.org/10.2307/1912517
7. Doğan, İ., & İltaş, Y. (2025). Döviz kurları ile CDS primleri arasındaki volatilite yayılımları: Kırılgan beşli ülkelerinden kanıtlar. Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 70, 125-132. https://doi.org/10.18070/erciyesiibd.1621363
8. Enders, W., & Jones, P. (2016). Grain prices, oil prices, and multiple smooth breaks in a VAR. Studies in Nonlinear Dynamics & Econometrics, 20(4), 399–419. https://doi.org/10.1515/snde-2014-0101

9. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007. https://doi.org/10.2307/1912773
10. Engle, R. F. (2001). GARCH 101: The use of ARCH/GARCH models in applied econometrics. Journal of Economic Perspectives, 15(4), 157–168. http://dx.doi.org/10.1257/jep.15.4.157
11. Engle, R. F., & Rangel, J. G. (2008). The spline-GARCH model for low-frequency volatility and its global macroeconomic causes. The Review of Financial Studies, 21(3), 1187–1222. http://dx.doi.org/10.2139/ssrn.939447
12. Hafner, C. M., & Herwartz, H. (2006). A Lagrange multiplier test for causality in variance. Economics Letters, 93(1), 137–141. https://doi.org/10.1016/j.econlet.2006.04.008
13. Hansen, P. R., & Lunde, A. (2005). A forecast comparison of volatility models: Does anything beat a GARCH (1,1)? Journal of Applied Econometrics, 20(7), 873–889. https://doi.org/10.1002/jae.800
14. Li, J., & Enders, W. (2018). Flexible fourier form for volatility breaks. Studies in Nonlinear Dynamics & Econometrics, 22(1), 1–19. https://doi.org/10.1515/snde-2016-0039
15. Nazlioglu, S., Gupta, R., Gormus, A., & Soytas, U. (2020). Price and volatility linkages between international REITs and oil markets. Energy Economics, 88, 104779. https://doi.org/10.1016/j.eneco.2020.104779
16. Özdemir, K., & Taş, H. (2025). Investor attention and its impact on portfolio volatility and sectoral risk spillovers in Borsa Istanbul. Borsa Istanbul Review, 25(1), 107–126. https://doi.org/10.1016/j.bir.2024.12.014
17. Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346. https://doi.org/10.1093/biomet/75.2.335
18. Sahoo, S., & Kumar, S. (2024). Volatility spillover among the sectors of emerging and developed markets: a hedging perspective. Cogent Economics & Finance, 12(1), 1-17. https://doi.org/10.1080/23322039.2024.2316048
19. Uluceviz, E. (2024). Borsa Istanbul sectoral connectedness analysis. Yönetim ve Ekonomi Dergisi, 31(1), 61-74. https://doi.org/10.18657/yonveek.1284521
20. Zhao, W., & Gao, Y. (2024). Dynamic patterns and the latent community structure of sectoral volatility and jump risk contagion. Emerging Markets Review, 59, 101110. https://doi.org/10.1016/j.ememar.2024.101110