Modeling Istanbul Stock Exchange-100 Daily Stock Returns: A Nonparametric Garch Approach

Abstract

Autoregressive conditional heteroscedasticity (ARCH) and Generalized ARCH (GARCH) models with various alternatives have been widely analyzed in the finance literature in order to model the volatility of the returns. In all of these models, the hidden variable volatility depends parametrically on lagged values of the process and lagged values of volatility (Bühlmann and McNeill, 2002) where the parameters are estimated with a nonlinear maximum likelihood function. In this paper a nonparametric approach to GARCH models proposed by Bühlmann and McNeill (2002) is followed to model the volatility of daily stock returns of the Istanbul Stock Exchange 100 (ISE 100) market from January 1991 to November 2012.

Keywords

• ARCH-GARCH modeling,nonparametric GARCH,unit root,ARMA,stock returns,ISE 100.

References

1. Andersen, T. G., Bollerslev, T., Diebold, F.X. (2002). Parametric and Nonparametric Volatility
2. Measurement. NBER Technical Working Paper, Paper No. 279. Atakan, T. (2009). The Modelling of Volatility at the Istanbul Stock Exchange with ARCHGARCH Models (in Turkish).Yönetim ,20 (62), 48-61.
3. Auestad, B., Tjİstheim, D. (1990). Identification of Nonlinear Time Series: First Order
4. Characterization and Order Determination. Biometrika, 77(4), 669-687. Balaban, E., Candemir, H.B., Kunter, K. (1996), Estimation of Monthly Fluctuation in Istanbul
5. Stock Exchange Market (in Turkish: Istanbul Menkul Kıymetler Borsası’nda Aylık Dalgalanma Tahmini),T. C.Merkez Bankası Müdürlüğü. Tartışma Tebliği(No. 9609). URL: http://www.tcmb.gov.tr/research/discus/9609tur.pdf
6. Balaban, E. (1999). Forecasting Stock Market Volatility: Evidence from Turkey. Unpublished
7. Manuscript, Central Bank of the Republic of Turkey, and JW Goethe University, Frankfurt/Main, Germany. Bellini, F., Figa-Talamanca, G. (2004). Detecting and modeling tail dependence. International
8. Journal of Theoretical and Applied Finance, 7(3), 269-287. Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity.Journal of Econometrics, 31, 307-327.

9. Bühlmann, P., McNeill, A.J. (2002). An Algorithm for Nonparametric GARCH Modelling.
10. Computational Statistics and Data Analysis, 40(4), 665-683. Chen, S.X., Tang, C.Y. (2005). Nonparametric Inference of Value-At-Risk for Dependent
11. Financial Returns. Journal of Financial Econometrics, 3(2), 227-255. DiSario, R., Saraoglu, H., McCarthy, J., Li, H. (2008). Long Memory in The Volatility of An
12. Emerging Equity Market: The Case of Turkey. Journal of International Financial Markets, Institutions and Money, 18(4), 305-312. Engle, R. (1982). Autoregressive Conditional HeteroskedasticityWith Estimates of the Variance of
13. UK Inflation. Econometrica, 50(4), 987-1007.
14. Engle, R.F., Gonzalez-Rivera, G. (1991). Semiparametric ARCH models.Journal of Business and Economic Statistics, 9(4), 345-359.
15. Gökçe, A. (2001). Measurement of Istanbul Stock Exchange Market Return Volatility with ARCH
16. Methods (in Turkish: İstanbul Menkul Kıymetler Borsası Getirilerindeki Volatilitenin ARCH Teknikleri ile Ölçülmesi), GaziÜniversitesi İ.İ.B.F Dergisi, 1, 33-58. Graves, S. (2012). FinTS: Companion to Tsay (2005) Analysis of Financial Time Series. R package version 0.4-4, URL http://cran.r-project.org/web/packages/FinTS/index.html.
17. Härdle, W., Chen, R. (1995). Nonparametric Time Series Analysis, a Selective Review with
18. Examples. Proceedings of the 50th Session of the ISI. Härdle, W., Lütkepohl, H., Chen, R. (1997).A Review of Nonparametric Time Series
19. Analysis. International Statistical Review/Revue Internationale de Statistique, 65(1), 49-72. Hou, A., Suardi S. (2012). A Nonparametric GARCH Model Of Crude Oil Price Return Volatility.
20. Energy Economics, 34(2), 618-626. Kalaycı, Ş. (2005). The Volatility Relationship Between Stock Market and Economy: A
21. Conditional Variance Analysis in the Istanbul Stock Exchange (in Turkish). SüleymanDemirelÜniversitesiİktisadiveİdariBilimlerFakültesiDergisi, 10(1), 241-250. Kilic, R. (2004). On The Long Memory Properties Of Emerging Capital Markets: Evidence From
22. Istanbul Stock Exchange. Applied Financial Economics, 14(13), 915-922. Korkmaz, T., Aydın, K. (2002). Using EWMA And GARCH Methods In VaR Calculations: Application on ISE-30 Index. ERC/METU 6. International Conference in Economics, September 11-14, 2002, Ankara.
23. Mazıbaş, M. (2005). Modelling and Estimation of ISE Volatility: An Application with
24. Asymmetric GARCH Models (in Turkish: İMKB Piyasalarındaki Volatilitenin Modellenmesi ve Öngörülmesi: Asimetrik GARCH Modellerile bir Uygulama). İstanbul Üniversitesi Ekonometri ve İstatistik Sempozyumu, 7 Mayıs, 26-27. Özden, Ü. (2008). Analysis of Istanbul Stock Exchange 100 Index's Return Volatility (in
25. Turkish).İstanbul Ticaret Üniversitesi Sosyal Bilimler Dergisi, 7(13), 339-350. Pfaff, B., Stigler, M. (2011). urca: Unit root and cointegration tests for time series data. R package version 1.2-5, URL http://cran.r-project.org/web/packages/urca/index.html.
26. R (2008): A Language and Environment for Statistical Computing, R Development Core Team, R
27. Foundation for Statistical Computing, Vienna, Austria, URL: http://www.R-project.org . Rüzgar, B., Kale, İ. (2007). The Use of ARCH and GARCH Models for Estimating and Forecasting Volatility. Kocaeli Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 14(2), 78-109.
28. Sarıkovanlık, V. (2006).GARCH Volatility Forecasting From Autoregressive Models (in
29. Turkish).Yönetim Dergisi, 17(54), 3-16. Sarıoğlu, S. E. (2006). Volatility Models and Cross Sectional Examination of the Volatility
30. Models in ISE Market (in Turkish: Değişkenlik Modellerive İMKB Hisse Senetleri Piyasası'nda Değişkenlik Modellerinin Kesitsel Olarak İrdelenmesi). Published Ph.D. Thesis. İktisadi Araştırmalar Vakfı. Sevüktekin, M., Nargeleçekenler, M. (2006). Modelling and Forecasting of Return Volatility at
31. İstanbul Stock Exchange (in Turkish). Ankara Üniversitesi SBF Dergisi, 61(4), 243-265. Tjİstheim, D., Auestad, B.H. (1994). Nonparametric Identification of Nonlinear Time Series: Projections. Journal of the American Statistical Association, 89(428), 1398-1409.
32. Trapletti, A., Hornik, K., LeBaron, B.(2012). tseries: Time Series Analysis and Computational
33. Finance. R package version 0.10-30, URL http://cran.r-project.org/web/packages/tseries/index.html. Tsay, R. (2002). Analysis of Financial Time Series Financial Econometrics. USA: John Wiley & Sons.
34. Tschernig, R., Yang, L. (2000). Nonparametric Lag Selection for Time Series. Journal of Time
35. Series Analysis, 21(4), 457–487. Wang, L., Feng, C., Song, Q., Yang, L. (2012). Efficient Semiparametric GARCH Modeling Of
36. Financial Volatility. Statistica Sinica, 22, 249-270. Wei, Y., Wang, Y., Huang, D. (2010). Forecasting crude oil market volatility: Further evidence using GARCH-class models. Energy Economics , 32, 1477–1484.
37. Yalçın, Y. (2007). An Examination of the Leverage Effect in the ISE with Stochastic Volatility
38. Model (in Turkish). Dokuz Eylül Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 22(2), 357-3 Yang, L., Härdle, W., Nielsen, J. (1999). Nonparametric Autoregression with Multiplicative
39. Volatility and Additive Mean. Journal of Time Series Analysis, 20(5), 579-604.