BİST100 ENDEKSİ FİYAT ve İŞLEM HACMİNİN FRAKTALLIK ANALİZİ

Bu çalışmada 04.01.2000-19.03.2014 dönemi için BIST100 Endeksi’nin getirileri ve işlem hacminin fraktal yapısı incelenmiştir. Fraktallık testlerinde uzun dönemli bellek analizleri ve fraktal boyut hesaplama yöntemleri kullanılmıştır. Uzun dönemli bellek hesaplamalarında Dönüştürülmüş Genişlik analizi, Eğilimden Arındırılmış Dalgalanma Analizi ve Smith’in 2005 modifiye GPH analizi kullanılırken, fraktal boyut hesaplamalarında Kutu Sayım,Yarı-Periyodogram ve Variogram yöntemleri uygulanmıştır. Elde edilen sonuçlar tüm yöntemler için tutarlı olup, hem BIS100 endeks getirlerinde hem de işlem hacminde fraktal bir yapı olmadığı görülmüştür.

Anahtar Kelimeler:

Uzun Dönemli Bellek, Fraktal Boyut, Kendine Benzerlik, Fraktallık

FRACTALITY ANALYSIS of BIST100 INDEX RETURNS and VOLUME

In this study, we examined the fractal structure of the BIST100 index returns and volume during the period of 04.01.2000-19.03.2014. In the fractality tests we used long memory analysis and the fractal dimension calculation methods. Long memory analysis was conducted via Rescaled Range R/S analysis, Detrended Fluctuaiton Analysis DFA and Smith’s 2005 modified GPH analysis; fractal dimension calculations were performed with Box-Counting, Semi-Periodogram and Variogram methods. Results showed that all findings of the different methods consistent with each other, and there is no fractality in the BIST100 index returns and volume

Keywords:

Long Memory, Fractal Dimension, Self-Similarity, Fractality,

___

BAILLIE, R.T., BOLLERSLEV, T., MIKKELSEN, H.O. (1996). Fractionally integrated generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 74, 3- 30. ss.
BARKOULAS, J.T., BAUM, C.F. (1997). Long memory and forecasting in euroyen deposit rates. Financial Engineering and the Japanese Markets, 4 (3), 189-201. ss.
BARKOULAS, J.T., BAUM, C.F., ÇAĞLAYAN, M. (1998). Fractional monetary dynamics. Boston College Working Papers in Economics, 321, 1-21. ss.
BAYRAKTAR, E., POOR, H.V., SIRCAR, K.R. (2004). Estimating the fractal dimension of the S&P 500 index using wavelet analysis. International Journal of Theoretical and Applied Finance, 7(5), 613-643.ss.
BO, C., ZHONGYONG, Y. (2007). On the fractal analysis of listed military industry capital market. International Conference on Management Science and Engineering, Finance Analysis, 281-288. ss.
CAVALCANTE, J., 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.
FAMA, E. (1965). Random walks in stock market prices. Financial Analysis Journal, 76, 75- 80. ss.
FOCARDI, S.M., FABOZZI, F.J. (2004). The mathematics of financial modeling and investment management. New Jersey, John Wiley & Sons.
FOO, D.A.C. (2009). Modeling market memory as potential indicators of market informational efficiency. 18th World Imacs / Modsim Congress, Australia, 2009, s.1307- 1313. ss.
GAYATHRI, M., SELVAM, M., LINGARAJA, K., VASANTH V., KARPAGAM, V. (2013). Fractal dimension Of S&P Cnx nifty stock returns. Asian Journal of Empirical Research, 3(9), 1166-1190. ss.
GEWEKE, J., PORTER-HUDAK, S. (1983). The estimation and appication of long memory time series models. Journal of Time Series Analysis, 4 (4), 221-238. ss.
GIRAITIS, L., KOKOSZKA, P., LEIPUS, R., TEYSSIERE, G. (2003). Rescaled variance and related tests for long memory in volatility and levels. Journal of Econometrics, 112 (2), 265-294. ss.
GNEITING, T., SEVCIKOVA, H., PERCIVAL, D.B. (2012). Estimators of fractal dimension : assessing the roughness of time series and spatial data. Statistical Science, 27 (2), 247– 277. ss.
GRANGER, C.W.J., JOYEUX, R. (1980). An introduction to loag memory time series models and fractional differencing. Journal of Time Series Analysis, 1, 5-39. ss.
GREENE, M.T., FIELITZ, B.D. (1977). Long-term dependence in common stock returns. Journal of Financial Economics, 4 (3), 339-349. ss.
HERGARTEN, S. (2002). Self-organized criticality in earth systems. Germany, Springer.
HIEMSTRA, C., JONES, J. D. (1997). Another look at long memory in common stock returns. Journal of Empirical Finance, 4 (4), 373-401. ss.
HOSKING, J.R.M. (1981). Fractional differencing. Biometrika, 68, 165-176.. ss.
HURST, H.E. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770-808. ss.
KANTELHARDT, J.W., KOSCIELNY-BUNDE, E., REGO, H.H.A., HAVLIN, S., BUNDE A. (2001). Detecting long-range correlations with detrended fluctuation analysis. Physica A, 295, 441–454. ss.
KIM, B.S., KIM, H.S., MIN, S.H. (2014). Hurst’s memory for chaotic, tree ring, and SOI series. Applied Mathematics, 5, 175-195. ss.
KOTOWSKI, S., KOSINSKI, W., MICHALEWICZ, Z., NOWICKI, J., PRZEPIORKIEWICZ, B. (2008). Fractal dimension of trajectory as invariant of genetic algorithms. Artificial Intelligence and Soft Computing – ICAISC 2008, 414-425. ss.
KRISTOUFEK, L., VOSVRDA, M.. (2013). Measuring capital market efficiency: long-term memory, fractal dimension and approximate entropy. Proceedings of the 31th International Conference Mathematical Methods in Economics, 470-475. ss.
KUMAR, D., MAHESWARAN, S. (2012). Long memory in PIIGS economies: an application of wavelet analysis. Management Review, 4 (95), 21-34. ss.
LO, A.W. (1991). Long-term memory in stock market prices. Econometrica, 59 (5), 1279- 1313. ss.
MANDELBROT B.B., HUDSON, R.L. (2006). Finans piyasalarında saklı düzen risk, çöküş ve kazanca fraktal yaklaşımlar. (Çev. M. HÜNER) İstanbul, Güncel Yayıncılık.
MANDELBROT, B. B. (1963). The variation of certain speculative prices. Journal of Business, 36, 392–417. ss.
MANDELBROT, B.B. (1972). Statistical methodology for nonperiodic cycles from covariance to R/S analysis. Annals of Economic and Social Measurement, 1, 259-290. ss.
MANDELBROT, B.B. (1983). The fractal geometry of natüre. New York, W. H. Freeman.
MANDELBROT, B.B., WALLIS J.R. (1969a). Computer experiments with fractional Gaussian noises: averages and variances. Water Resources Research, 5(1), 228–241. ss.
MIKOSCH, T., STARICA, C. (1999). Change of structure in financial time series, long range dependence and the GARCH Model. Working Paper, The Wharton School, Chalmers University of Technology.
OSWIECIMKAA, P., DROZDZA, S., KWAPIENA, J., GÓRSKI A.Z. (2010). Fractals, log- periodicity and financial crashes. Acta Physica Polonica A,117 (4), 637-639. ss.
PENG, C.K., BULDYREV, S.V., HAVLIN, S., SIMONS, M., STANLEY, H.E., GOLDBERGER A.L. (1994). Mosaic organization of DNA nucleotides. Phys. Rev. E, 49 (2), 1685–1689.ss.
PETERS, E. (1994). Fractal market analysis - applying chaos theory to investment and analysis. New York, John Wiley & Sons, Inc.
REGE, S., MARTIN, S.G.. (2011). Portuguese stock market: a long memory process?. Business: Theory and Practice, 12 (1), 75-84. ss.
RELJIN, I.S., RELJIN, B.D. (2002). Fractal geometry and multifractals in analyzing and processing medical data and images. Archive of Oncology, 10, (4), 2002, s.283-293. ss.
SMITH, A. (2005). Level shifts and the illusion of long memory in economic time series. Journal of Business & Economic Statistics, 23 (3), 321-335. ss.
SORNETTE, D. (2003). Critical phenomena in natural sciences: chaos, fractals, selforganization and disorder: concepts and tools. New York, Springer Verlag.
TEL, T. (1988). Fractals, multifractals, and thermodynamics an itroductory review. Z. Naturforsch, 43a, 1154-1174. ss.
TSUJI, C. (2003). Long term memory and applying the multi-factor ARFIMA models to financial markets. Asia Pasific Financial Markets, 9, 283-304. ss.
WERON, R. (2002). Estimating long-range dependence: finite sample properties and confidence intervals. Physica A, 312, 285 – 299. ss.
WILLIAMS, B. (1995). Trading chaos. New Jersey, John Wiley&Sons.
WILLIAMS, G. P. (1997). Chaos theory tamed. Washington, Joseph Henry Press,
WILLINGER, W., TAQQU, M. S., TEVEROVSKY, V. (1999). Stock market prices and long-range dependence. Finance and Stochastics, 3 (1), 1-13. ss.