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Fractal Structure of the Stock Markets of Leading Asian Countries

Samet Günay
대외경제정책연구원 (Korea Institute for International Economic Policy (KIEP))|2014.12|East Asian Economic Review|제18권 제4호|pp. 367-394|DOI http://dx.doi.org/10.11644/KIEP.JEAI.2014.18.4.286

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참고문헌

키워드

Long MemoryAsian Stock MarketsFractal DimensionSelf-SimilarityFractal Structure
주제분류경제학

초록

In this study, we examined the fractal structure of the Nikkei225, HangSeng, Shanghai Stock Exchange and Straits Times Index of Singapore. Empirical analysis was performed via non-parametric, semi-parametric long memory tests and also fractal dimension calculations. In order to avoid spurious long memory features, besides the Detrended Fluctuations Analysis (DFA), we also used Smith’s (2005) modified GPH method. As for fractal dimension calculations, they were conducted via Box-Counting and Variation tests. According to the results, while there is no long memory property in log returns of any index, we found evidence for long memory properties in the volatility of the HangSeng, the Shanghai Stock Exchange and the Straits Times Index. However, we could not find any sign of long memory in the volatility of Nikkei225 index using either the DFA or modified GPH test. Fractal dimension analysis also demonstrated that all raw index prices have fractal structure properties except for the Nikkei225 index. These findings showed that the Nikkei225 index has the most efficient market properties among these markets.

Abstract

In this study, we examined the fractal structure of the Nikkei225, HangSeng, Shanghai Stock Exchange and Straits Times Index of Singapore. Empirical analysis was performed via non-parametric, semi-parametric long memory tests and also fractal dimension calculations. In order to avoid spurious long memory features, besides the Detrended Fluctuations Analysis (DFA), we also used Smith’s (2005) modified GPH method. As for fractal dimension calculations, they were conducted via Box-Counting and Variation tests. According to the results, while there is no long memory property in log returns of any index, we found evidence for long memory properties in the volatility of the HangSeng, the Shanghai Stock Exchange and the Straits Times Index. However, we could not find any sign of long memory in the volatility of Nikkei225 index using either the DFA or modified GPH test. Fractal dimension analysis also demonstrated that all raw index prices have fractal structure properties except for the Nikkei225 index. These findings showed that the Nikkei225 index has the most efficient market properties among these markets.

참고문헌 (73)

  1. Robust Testing for Fractional Integration Using the Bootstrap, "Andersson, M. K.", Stockholm School of Economics, ~, pp.Working Paper Series in Economics and Finance218 (1998)
  2. Bachelier, L., "Théorie de la speculation", Annales Scientifiques de L’École Normale Supérieure, 17, pp.21~86 (1900)
  3. Baillie, R. T., "Long memory processes and fractional integration in econometrics", Journal of Econometrics, 73(1), pp.5~59 (1996)
  4. Baillie, R. T., "Fractionally integrated Generalized Autoregressive Conditional Heteroskedasticity", Journal of Econometrics, 74(1), pp.3~30 (1996)
  5. Baillie, R. T., "Modelling long memory and structural breaks in conditional variances : An adaptive FIGARCH approach", Journal of Economic Dynamics and Control, 33(8), pp.1577~1592 (2009)
  6. Bhattacharya, S. N., "Long Memory in Stock Returns : A Study of Emerging Markets", Iranian Journal of Management Studies, 5(2), pp.67~88 (2012)
  7. Black, F., "The Pricing of Options and Corporate Liabilities", Journal of Political Economy, 81(3), pp.637~654 (1973)
  8. Cajueiro, D. O., "Evidence of long range dependence in Asian equity markets: the role of liquidity and market restrictions", Physica A, 342(3-4), pp.656~664 (2004)
  9. Chaitip, P., "On Tests For Long-Term Dependence: India’s International Tourism Market", Applied Studies in Agribusiness and Commerce, 5(1-2), pp.110~111 (2011)
  10. Cheung, Y. W., "Long memory in foreign-exchange rates", Journal of Business & Economic Statistics, 11(1), pp.93~101 (1993)
  11. Choi, S., "The Performance of the GPH Estimator of the Fractional Difference Parameter : Simulation Results", Review of Quantitative Finance and Accounting, 2(4), pp.409~417 (1992)
  12. Choi, K., "Long memory versus structural breaks in modeling and Forecasting realized volatility", Journal of International Money and Finance, 29(5), pp.857~875 (2010)
  13. Deboeck, G. J., "Trading on the Edge: Neural, Genetic, and Fuzzy Systems for Chaotic Financial Markets" (1994), John Wiley & Sons
  14. Ding, Z. C., "A Long Memory Property of Stock Market Returns And A New Model", Journal of Empirical Finance, 1(1), pp.83~106 (1993)
  15. Engel, C., "Long Swings in The Dollar : Are They in The Data And Do Markets Know It?", American Economic Review, 8(4), pp.689~713 (1990)
  16. Fama, E., "Random Walks in Stock Market Prices", Financial Analysts Journal, 21(5), pp.55~59 (1965)
  17. Fama, E., "Efficient Capital Markets : a Review of Theory and Empirical Work", Journal of Finance, 25(2), pp.383~417 (1970)
  18. Farmer, J. D., "Beyond Equilibrium and Efficiency" (2002), Oxford University Press
  19. Geweke, J., "The Estimation and Application of Long Memory Time Series Models", Journal of Time Series Analysis, 4(4), pp.221~238 (1983)
  20. Gil-Alana, L. A., "On the persistence and volatility in European, American and Asian stocks bull and bear markets", Journal of International Money and Finance, 40, pp.149~162 (2014)
  21. Giraitis, L., "Testing for Long Memory in the Presence of a General Trend", Journal of Applied Probability, 38(4), pp.1033~1054 (2001)
  22. Gneiting, T., "Estimators of Fractal Dimension : Assessing the Roughness of Time Series and Spatial Data", Statistical Science, 27(2), pp.247~277 (2012)
  23. Grabbe, J. O., "Chaos and Fractals in Financial Markets: Grow Brain and the Flooding of the Nile", Laissez Faire City Times, 5(3) (2001)
  24. Structural Breaks and Long Memory, "Granger, C. W. J.", UCSD, ~, pp.Discussion Paper, 99-14 (1999)
  25. Granger, C. W. J., "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns", Journal of Empirical Finance, 11(3), pp.399~421 (2004)
  26. Granger, C. W. J., "An introduction to long memory time series models and fractional differencing", Journal of Time Series Analysis, 1(1), pp.15~29 (1980)
  27. Greene, M. T., "Long-term dependence in common stock returns", Journal of Financial Economics, 4(3), pp.339~349 (1977)
  28. Guggenberger, P., "Bias-Reduced Log-Periodogram and Whittle Estimation of the Long-Memory Parameter Without Variance Inflation", Econometric Theory, 22(5), pp.863~912 (2006)
  29. Hamilton, J. D., "Autoregressive Conditional Heteroskedasticity and Changes in Regime", Journal of Econometrics, 64(1-2), pp.307~333 (1994)
  30. 한영욱, "Structural Breaks and Long Memory Property in Korean Won Exchange Rates: Adaptive FIGARCH Model", Journal of East Asian Economic Integration, 15(2), pp.33~59 (2011), 대외경제정책연구원
  31. Hiemstra, C., "Another look at long memory in common stock returns", Journal of Empirical Finance, 4(4), pp.373~401 (1997)
  32. Hosking, J. R. M., "Fractional differencing", Biometrika, 68(1), pp.165~176 (1981)
  33. Hurst, H. E., "Long-term storage capacity of reservoirs", Transactions of the American Society of Civil Engineers, 116, pp.770~808 (1951)
  34. Jiang, Z., "Detecting mental EEG properties using detrended fluctuation analysis", Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference, pp.2017~2020 (2005)
  35. 강상훈, "Sudden Changes in Variance and Volatility Persistence in Asian Foreign Exchange Markets", Korea and the World Economy, 11(1), pp.129~143 (2010), 한국경제연구학회
  36. 강상훈, "Asymmetric Long Memory Feature in the Volatility of Asian Stock Markets", Asia-Pacific Journal of Financial Studies, 35(5), pp.175~198 (2006), 한국증권학회
  37. Kantelhardt, J. W., "Detecting long-range correlations with detrended fluctuation analysis", Physica A, 295(3-4), pp.441~454 (2001)
  38. Kim, B. S., "Hurst’s Memory for Chaotic Tree Ring, and SOI Series", Applied Mathematics, 5(1), pp.175~195 (2014)
  39. Kristoufek, L., "Rescaled Range Analysis and Detrended Fluctuation Analysis : Finite Sample Properties and Confidence Intervals", AUCO Czech Economic Review, 4(3), pp.315~329 (2010)
  40. LeBaron, B., "Stochastic volatility as a simple generator of apparent financial power laws and long memory", Quantitative Finance, 1(6), pp.621~631 (2001)
  41. Lee, C. W., "Existence of Persistent Temporal Dependence in Asian Emerging Markets Exchange-Traded Funds(ETFS)", International Journal of Research in Finance & Marketing, 4(7), pp.19~35 (2014)
  42. Lo, A. W., "Long-term memory in stock market prices", Econometrica, 59(5), pp.1279~1313 (1991)
  43. Lobato, I. N., "Real and Spurious Long-Memory Properties of Stock-Market Data", Journal of Business & Economic Statistics, 16(3), pp.261~268 (1998)
  44. Mandelbrot, B. B., "The variation of certain speculative prices", Journal of Business, 36(4), pp.394~419 (1963)
  45. Mandelbrot, B. B., "Statistical Methodology for Nonperiodic Cycles from Covariance to R", S Analysis, 1972, pp.1(3), 259~290
  46. Mandelbrot, B. B., "The fractal geometry of nature" (1983), W. H. Freeman
  47. Mandelbrot, B. B., "The Misbehavior of Markets: A Fractal View of Financial Turbulence" (2004), Basic Books
  48. Mandelbrot, B. B., "Noah, Joseph, and Operational Hydrology", Water Resources Research, 4(5), pp.909~918 (1968)
  49. Markowitz, H., "Portfolio selection", Journal of Finance, 7(1), pp.77~91 (1952)
  50. Change of Structure in Financial Time Series, Long Range Dependence and GARCH Model, "Mikosch, T.", University of Groningen, Department of Mathematics, ~, pp.Technical Report (1998)
  51. Murdzek, R, "The Box-Counting Method in the Large Scale Structure of the Universe", Romanian Journal of Physics, 52(1-2), pp.149~154 (2007)
  52. Ohanissian, A., "True or Spurious Long Memory? A New Test", Journal of Business & Economic Statistics, 26(2), pp.161~175 (2008)
  53. Peng, C. K., "Mosaic organization of DNA nucleotides", Physical Review E, 49(2), pp.1685~1689 (1994)
  54. Peters, E. E., "Fractal Market Analysis: Applying Chaos Theory to Investment and Economics" (1994), John Wiley & Sons
  55. Peters, E. E., "Chaos and Order in the Capital Markets" (1996), John Wiley & Sons
  56. Discrete Fourier transforms of fractional processes, "Phillips, P. C. B. 1999. Discrete Fourier transforms of fractional processes. Unpublished working paper No.", Cowles Foundation for Research in Economics, Yale University, ~, pp.working paper No. 1243 (1999)
  57. Unit root log periodogram regression, "Phillips, P. C. B.", Cowles Foundation for Research in Economics, Yale University, ~, pp.working paper No. 1244 (1999)
  58. Ratkowsky, D. A., "Modeling Microbial Responses in Food" (2004), CRC Press
  59. Ramasamy, R., "Chaotic Behavior of Financial Time Series-An Empirical Assessment", International Journal of Business and Social Science, 2(3), pp.77~83 (2011)
  60. Rege, S., "Portuguese stock market : A long Memory Process?", Business : Theory and Practice, 12(1), pp.75~84 (2011)
  61. Robinson, P. M., "Log-periodogram regression of time series with long range dependence", Annals of Statistics, 23(3), pp.1048~1072 (1995)
  62. Sharpe, W. F., "Capital Asset Prices : A Theory of Market Equilibrium Under Conditions of Risk", Journal of Finance, 19(3), pp.425~442 (1964)
  63. Smith, A., "Level Shifts and the Illusion of Long Memory in Economic Time Series", Journal of Business & Economic Statistics, 23(3), pp.321~335 (2005)
  64. Sriboonchitta, S., "On Tests for Long Memory Process Behavior of International Tourism Market: Thailand and India", Applied Studies in Agribusiness and Commerce, 5(3-4), pp.95~100 (2011)
  65. Tan, P. P., "Are Asia-Pacific Stock Markets Predictable? Evidence from Wavelet-based Fractional Integration Estimator", International Journal of Social, Management, Economics and Business Engineering, 5(11), pp.305~309 (2011)
  66. Tapiero, C. S., "Risk Finance and Asset Pricing: Value, Measurements, and Markets" (2010), John Wiley and Sons
  67. Vandewalle, N., "Detrended Fluctuation Analysis of the Foreign Exchange Market", Proceedings of Econophysic Workshop (1997)
  68. Velásquez, T., "Chaos Theory and the Science of Fractals, and their Application in Risk Management", tjrtk, pp.2009
  69. Weron, R, "Estimating long-range dependence: Finite sample properties and confidence intervals", Physica A, 312(1-2), pp.285~299 (2002)
  70. Weron, R., "DFA Calculate the Hurst exponent using DFA analysis", Matlab Code, ~ (2011)
  71. Willinger, W., "Stock market prices and long-range dependence", Finance and Stochastics, 3(1), pp.1~13 (1999)
  72. Witt, A., "Quantification of Long-Range Persistence in Geophysical Time Series: Conventional and Benchmark-Based Improvement Techniques", Surveys in Geophysics, 34(5), pp.541~651 (2013)
  73. Yalama, A., "Real or spurious long memory characteristics of volatility : Empirical evidence from an emerging market", Economic Modelling, 30, pp.67~72 (2013)

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