YAPISAL KIRILMALAR DAHİLİNDE BİST-100 ENDEKSi VOLATİLİTESİNİN UZUN DÖNEMLİ BELLEK ANALİZİ

Bu çalışmada BİST-100 Endeksi’nin volatilitesindeki uzun dönemli bellek yapısı incelenmiştir. Uzun dönemli bellek analizi fraktallığın göstergelerinden birisi olup, aynı zamanda Etkin Piyasa Hipotezi’nin zayıf formunun testinde de kullanılmaktadır. Çalışmanın ekonometrik analizi BİST-100 Endeksi’nin 03.01.1990-15.05.2013 zaman aralığındaki kareli ve mutlak getirileri ile FIGARCH modeli üzerinden yapılmış olup, yapısal kırılmaların varlığı sahte uzun dönemli bellek etkisi yaratabileceğinden, testler Bai-Perron çoklu yapısal kırılma testi öncesi ve sonrası olmak üzere iki kez gerçekleştirilmiştir. Elde edilen sonuçlar, incelenen dönem içerisinde BİST-100 Endeksi’nin volatilitesinde uzun dönemli belleğin varlığını ortaya koymuştur.

Anahtar Kelimeler:

Uzun Dönemli Bellek, Yapısal Kırılmalar, FIGARCH, Bai-Perron Test

LONG MEMORY ANALYSIS of the BIST-100 INDEX VOLATILITY INCLUSIVE of STRUCTURAL BREAKS

In this study, long memory structure of the BIST-100 Index volatility has been examined. Long memory is one of the indicators of fractality and also it is used to test the weak form of the Efficient Market Hypothesis. In the empirical part, we used squared and absolute returns of the BIST-100 Index during the period of 03.01.1990-15.05.2013. Econometric analysis was conducted via FIGARCH method. Since structural breaks can produce spurious long memory effect, all long memory tests were performed before and after Bai-Perron multiple break points analysis. Results exhibited that there is a long memory effect in the BIST-100 index volatility within the period of sample

Keywords:

Long Memory, Structural Breaks, FIGARCH, Bai-Perron Test,

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Andersen, T. G. and Bollerslev, T. (1997). Heterogeneous Information Arrivals And Return Volatility Dynamics:
Uncovering The Long-Run in High Frequency Returns. The Journal Of Finance, 52 (3). 975-1005
Andreou, E. and Ghysels, E. (2002). Detecting Multiple Breaks in Financial Market Volatility Dynamics. Journal of
Applied Econometrics, Cilt.17, Iss.5, 579-600
Aygören, H., (2008). İstanbul Menkul Kıymetler Borsasının Fractal Analizi. Dokuz Eylül Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, Cilt.23 (1), 125-134
Bai, J. ve Perron, P., (2003). Computation and Analysis of Multiple Structural Change Models. Journal of Applied Econometrics, Cilt.18, 1–22
Baillie, R. T., (1996). Long memory processes and fractional integration in econometrics. Journal of Econometrics, 73, 5-59
Baillie, R. T., Bollerslev, T. ve Mikkelsen H. O., (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, Cilt.74, 13-30
Beran, J. (1998). Statistics for Long Memory Processes. Chapman and Hall/Crc, Florida, s.42
Bhattacharya S. N. ve M. B., (2012). Long Memory in Stock Returns: A Study of Emerging Markets. Iranian
Journal of Management Studies, Cilt.5 (2), 67-88
Bollerslev, T. ve Mikkelsen H. O. (1996). Modeling and Pricing Long Memory in Stock Market Volatility. Journal
Of Econometrics, 73 (1), 151-184
Breidt, F. J., Crato, N. ve de Lima P. J. F. (1998). The detection and estimation of long-memory in stochastic in stochastic volatility. Journal of Econometrics, (83), 325–348
Cavalcante, J. and Assaf, A., (2002). Long Range Dependence in the Returns and Volatility of the Brazilian Stock
Market. Working Paper, Banco Nacional do Desenvolvimiento, Rio de Janeiro Choi, K, Yu W. C. and Zivot, E., (2010). Long memory versus structural breaks in modeling and Forecasting realized volatility. Journal of International Money and Finance, Cilt.29, 857–875
Comte, F. and Renault, E. (1998). Long Memory İn Continuous-Time Stochastic Volatility Models. Mathematical Finance, 8 (4): 291-323
Cotter, J., (2004). Absolute return volatility, University College Dublin. School of Business. Centre for Financial
Markets, WP-04-11, http://www.ucd.ie/bankingfinance/docs/wp/COTTER5.PDF Crato, N. ve de Lima, P. J. F. (1994). Long-range dependence in the conditional variance of stock returns.
Economics Letters, 45 (3): 281-285
Çevik, E. İ., (2012). İstanbul Menkul Kıymetler Borsası’nda Etkin Piyasa Hipotezinin Uzun Hafıza Modelleri İle
Analizi: Sektörel Bazda Bir İnceleme. The Journal of Yasar University, Cilt.26 (7), 4437- 4454
Çevik, E. İ. ve Erdoğan, S., (2009). Bankacılık Sektörü Hisse Senedi Piyasasının Etkinliği: Yapısal Kırılma ve Güçlü Hafıza. Doğuş Üniversitesi Dergisi, Cilt.10 (1), 26-40
Davidian, M. and Carroll, R.J. (1987). Variance function estimation. Journal of the American Statistical Association, 82, 1079–1091.
Diebold, F. X. ve Inoue, A. (2001). Long Memory And Regime Switching. Journal Of Econometrics, 105 (1), 131- 159
Ding, Z., Granger, C. W. J. ve Engle R. E. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1 (1), 83-106
Engle, R. F. ve Bollerslev, T.,(1986). Modelling the persistence of conditional variances. Econometric Reviews, Vol. 5 (1), 1-50
Engle, R. F. ve Patton, A. J., (2001). What good is a volatility model?. Quantitative Finance, Cilt. 1 (2), 237-245.
Fama, E. F. , (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. The Journal of Finance, Cilt.25 (2), 383-417
Festić, M., Kavkler, A. ve Dajčman, S., (2012). Long Memory in The Croatian And Hungarian Stock Market
Returns. Zb. Rad. Ekon. Fak. Rij, Cilt.30, Geweke, J. and Porter-Hudak, S. (1983). The estimation and Appication of Long Memory Time Series Models.
Journal of Time Series Analysis, Cilt.4 (4), 221-238. Granger, C.W.J. and Joyeux, R. (1980). An introduction to loag memory time series models and fractional differencing. Journal of Time Series Analysis,1, 5-39.
Ghysels, E., Santa-Clara, P. ve Valkanov, R., (2006). Predicting Volatility: Getting the Most Out of Return Data
Sampled at Different Frequencies. Journal of Econometrics, Cilt.131(1/2), 59-95. Giles, D. , (2008). Some properties of absolute returns as a proxy for volatility. Applied Financial Economics Letters, Cilt.4(5), 347-350.
Giraitis, L. et al. (2003). Rescaled Variance And Related Tests For Long Memory İn Volatility And Levels. Journal
Of Econometrics, Vol.112, No.2, 265-294. Grabbe, J. O. , (2001). Chaos and Fractals in Financial Markets: Grow Brain and the Flooding of the Nile. Laissez
Faire City Times, Cilt.5 (3) Granger, C.W.J. ve Hyung, N., (2004)., Occasional Structural Breaks And Long Memory With An Application To
The S&P 500 Absolute Stock Returns. Journal Of Empirical Finance, Vol.11, Iss.3, 399-421. Goudarzi, H. , (2010). Modeling Long Memory in The Indian Stock Market using Fractionally Integrated Egarch
Model. International Journal of Trade, Economics and Finance, Cilt.1(3), 231-237
Hosking, J.R.M. (1981). Fractional differencing. Biometrika, 68, 165-176.
Hurst, H. E., (1951). Long-term storage of reservoirs: An experimental study. Transactions of the American Society of Civil Engineers, 116, 770-799.
İlgün, M. F., (2010). Genişletici Mali Daralma Hipotezinin Temelleri ve Türkiye Ekonomisi Üzerine Bir Uygulama.
Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 35, 233-253
Kahyaoğlu, H. ve Duygulu, A. A. (2005). Finansal Varlık Fiyatlarındaki Değişme – Parasal Büyüklükler Etkileşimi.
Dokuz Eylül Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, Cilt.20 (1), 63-85
Kasman, A. ve Torun, E. (2007). Long Memory in the Turkish Stock Market Return and Volatility. Central Bank Review, (2), CBRT, 13-27
Kasman, A. , Kasman, S. ve Torun, E., (2009). Dual long memory property in returns and volatility: Evidence from the CEE countries' stock markets. Emerging Markets Review, Cilt.10, 122–139
Kirman, A and Teyssière, G. (2002). Microeconomic Models for Long Memory in the Volatility of Financial Time
Series. Studies in Nonlinear Dynamics and Econometrics, Vol.5, Iss.4, 1-23
Lee, D. ve Schmidt, P. (1996). On the power of the KPSS test of stationarity against fractionally-integrated alternatives. Journal of Econometrics, Cilt.73 (1), 285-302
Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics. Cilt. 47:1, 13–37.
Liu, S.M. ve Shieh, S.J. (2007). Long Memory in Volatility of T-Bond Futures Markets: A Value-at Ris Approach.
The Journal of Human Resource and Adult Learning, Cilt.3 (2), 2007, 225-233
Lobato, I. N. ve Savin, N. E. (1998). Real And Spurious Long-Memory Properties Of Stock-Market Data. Journal
Of Business & Economic Statistics, 16 (3), 261-268. Maekawa, K., Lee, S. ve Tokutsu, Y., (2005). A note on volatility persistence and structural changes in GARCH models. Working Paper, http://www.hue.ac.jp/prfssr/rcfe/w_papers/Rev23.pdf
Maheu, J. M., (2005). Can GARCH Models Capture the Long-Range Dependence in Financial Market Volatility?.
Studies in Nonlinear Dynamics & Econometrics, Cilt.9 (4), 1-40
Mandelbrot, B. (1972). Statistical methodology for nonperiodic cycles: from the covariance to R/S analysis. Annals of Economic and Social Measurement 1, 259–290.
Mandelbrot, B. ve Wallis J. R. , (1969). Computer Experiments with Fractional Gaussian Noises: Part 2, Rescaled
Ranges and Spectra. Water resources research, Cilt. 5(1), 242-259
Mandelbrot B. ve Hudson R. L. (2004). The Misbehavior of Markets: A fractal view of financial turbulence. Basic Books, New York.
Markowitz, H. (1952). Portfolio Selection. Journal of Finance. Cilt.7, 77–91.
Markowitz, H. (1959). Portfolio Selection: Effi cient Diversification of Investments. Second Edition. Malden: Blackwell.
Onali, E. ve Goddard J, (2011). Are European Equity Markets Efficient? New Evidence from Fractal Analysis.
International Review of Financial Analysis, 20, 59–67 Önalan, Ö., (2004). Finans Mühendisliğinde Matematiksel Modelleme. Avcıol Basım, 1. Baskı, İstanbul
Pagan, A. R. ve Schwert, G. W., (1990). Alternative Models For Conditional Stock Volatility. Journal of Econometrics, 45, 267-290
Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance. Cilt19 (3), 425– 42.
Tayefi, M. ve Ramanathan T. V., (2012). An Overview of FIGARCH and Related Time Series Models. Austrian
Journal of Statistics, Cilt.41 (3), 175-196
Triacca, U., (2007). On the variance of the error associated to the squared return as proxy of volatility. Applied
Financial Economics Letters, Cilt.3 (4), 255-7
Tunay, K. B. ,(2008). Türkiye’de Merkez Bankası Müdahalelerinin Döviz Kurlarının Oynaklığına Etkileri. BDDK
Bankacılık ve Finansal Piyasalar Dergisi, Cilt.2 (2), 77-111
Ural, M. ve Demireli E., (2009). Hurst Üstel Katsayısı Aracılığıyla Fraktal Yapı Analizi ve İMKB’de Bir
Uygulama. Atatürk Üniversitesi İktisadi ve İdari Bilimler Dergisi, Cilt.23 (2), 243-255
Velásquez, T., (2009). Chaos Theory and the Science of Fractals, and their Application in Risk Management.
Yüksek Lisans Tezi, Copenhagen Business School Yalama, A. Çelik, S. ve Sevil, G., (2011). Long Memory in Stock Markets: Empirical Study on Spot and Future
Markets in Turkey. Academic and Business Research Institute International Conference, International Conference- Las Vegas