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Unifractality and multifractality in the Italian stock market

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  • Onali, Enrico
  • Goddard, John

Abstract

Tests for random walk behaviour in the Italian stock market are presented, based on an investigation of the fractal properties of the log return series for the Mibtel index. The random walk hypothesis is evaluated against alternatives accommodating either unifractality or multifractality. Critical values for the test statistics are generated using Monte Carlo simulations of random Gaussian innovations. Evidence is reported of multifractality, and the departure from random walk behaviour is statistically significant on standard criteria. The observed pattern is attributed primarily to fat tails in the return probability distribution, associated with volatility clustering in returns measured over various time scales.

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  • Onali, Enrico & Goddard, John, 2009. "Unifractality and multifractality in the Italian stock market," International Review of Financial Analysis, Elsevier, vol. 18(4), pages 154-163, September.
    • Handle: RePEc:eee:finana:v:18:y:2009:i:4:p:154-163
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    as
    1. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    2. Tóth, Bence & Kertész, János, 2006. "Increasing market efficiency: Evolution of cross-correlations of stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 505-515.
    3. Kim, Kyungsik & Yoon, Seong-Min, 2004. "Multifractal features of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 272-278.
    4. Di Matteo, T. & Aste, T. & Dacorogna, M.M., 2003. "Scaling behaviors in differently developed markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 183-188.
    5. Lo, Andrew W & MacKinlay, A Craig, 1990. "When Are Contrarian Profits Due to Stock Market Overreaction?," The Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 175-205.
    6. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Long-range dependence and multifractality in the term structure of LIBOR interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 603-614.
    7. Greene, Myron T. & Fielitz, Bruce D., 1977. "Long-term dependence in common stock returns," Journal of Financial Economics, Elsevier, vol. 4(3), pages 339-349, May.
    8. Frennberg, Per & Hansson, Bjorn, 1993. "Testing the random walk hypothesis on Swedish stock prices: 1919-1990," Journal of Banking & Finance, Elsevier, vol. 17(1), pages 175-191, February.
    9. Natividad Blasco & Cristina Del Rio & Rafael Santamaría, 1997. "The Random Walk Hypothesis in the Spanish Stock Market: 1980-1992," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(5), pages 667-684.
    10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    11. Lee, Kyoung Eun & Lee, Jae Woo, 2007. "Probability distribution function and multiscaling properties in the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 65-70.
    12. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    13. Selçuk, Faruk & Gençay, Ramazan, 2006. "Intraday dynamics of stock market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 375-387.
    14. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    15. Oświe¸cimka, P. & Kwapień, J. & Drożdż, S., 2005. "Multifractality in the stock market: price increments versus waiting times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 626-638.
    16. Marshall, Ben R. & Cahan, Rochester H., 2005. "Is technical analysis profitable on a stock market which has characteristics that suggest it may be inefficient?," Research in International Business and Finance, Elsevier, vol. 19(3), pages 384-398, September.
    17. Norouzzadeh, P. & Jafari, G.R., 2005. "Application of multifractal measures to Tehran price index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 609-627.
    18. Groenewold, Nicolaas & Kan Tang, Sam Hak & Wu, Yanrui, 2008. "The profitability of regression-based trading rules for the Shanghai stock market," International Review of Financial Analysis, Elsevier, vol. 17(2), pages 411-430.
    19. Michael D. McKenzie, 2001. "Non‐periodic Australian Stock Market Cycles: Evidence from Rescaled Range Analysis," The Economic Record, The Economic Society of Australia, vol. 77(239), pages 393-406, December.
    20. Hoque, Hafiz A.A.B. & Kim, Jae H. & Pyun, Chong Soo, 2007. "A comparison of variance ratio tests of random walk: A case of Asian emerging stock markets," International Review of Economics & Finance, Elsevier, vol. 16(4), pages 488-502.
    21. Grech, Dariusz & Pamuła, Grzegorz, 2008. "The local Hurst exponent of the financial time series in the vicinity of crashes on the Polish stock exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4299-4308.
    22. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    23. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    24. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    25. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    26. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    27. Ojah, Kalu & Karemera, David, 1999. "Random Walks and Market Efficiency Tests of Latin American Emerging Equity Markets: A Revisit," The Financial Review, Eastern Finance Association, vol. 34(2), pages 57-72, May.
    28. Cheung, Yin-Wong & Lai, Kon S, 1993. "Do Gold Market Returns Have Long Memory?," The Financial Review, Eastern Finance Association, vol. 28(2), pages 181-202, May.
    29. Opong, Kwaku K. & Mulholland, Gwyneth & Fox, Alan F. & Farahmand, Kambiz, 1999. "The behaviour of some UK equity indices: An application of Hurst and BDS tests1," Journal of Empirical Finance, Elsevier, vol. 6(3), pages 267-282, September.
    30. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    31. Ané, Thierry & Ureche-Rangau, Loredana, 2008. "Does trading volume really explain stock returns volatility?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(3), pages 216-235, July.
    32. Alvarez-Ramirez, Jose & Cisneros, Myriam & Ibarra-Valdez, Carlos & Soriano, Angel, 2002. "Multifractal Hurst analysis of crude oil prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 651-670.
    33. Metghalchi, Massoud & Chang, Yung-Ho & Marcucci, Juri, 2008. "Is the Swedish stock market efficient? Evidence from some simple trading rules," International Review of Financial Analysis, Elsevier, vol. 17(3), pages 475-490, June.
    34. T. Ane & L. Ureche-Rangau, 2008. "Does Trading Volume Really Explain Stock Returns Volatility ?," Post-Print hal-00260668, HAL.
    35. Martin Laurence & Francis Cai & Sun Qian, 1997. "Weak-form Efficiency and Causality Tests in Chinese Stock Markets," Multinational Finance Journal, Multinational Finance Journal, vol. 1(4), pages 291-307, December.
    36. Eisler, Z. & Kertész, J., 2004. "Multifractal model of asset returns with leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 603-622.
    37. Fama, Eugene F, et al, 1969. "The Adjustment of Stock Prices to New Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(1), pages 1-21, February.
    38. Natividad Blasco & Cristina Del Rio & Rafael Santamaría, 1997. "The Random Walk Hypothesis in the Spanish Stock Market: 1980–1992," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(5), pages 667-684, June.
    39. Groenewold, Nicolaas & Tang, Sam Hak Kan & Wu, Yanrui, 2003. "The efficiency of the Chinese stock market and the role of the banks," Journal of Asian Economics, Elsevier, vol. 14(4), pages 593-609, August.
    40. Howe, John S. & Martin, Deryl W. & WoodJr., Bob G., 1999. "Much ado about nothing: Long-term memory in Pacific Rim equity markets," International Review of Financial Analysis, Elsevier, vol. 8(2), pages 139-151, June.
    41. Barone, E., 1990. "The italian stock market : Efficiency and calendar anomalies," Journal of Banking & Finance, Elsevier, vol. 14(2-3), pages 483-510, August.
    42. Norouzzadeh, P. & Rahmani, B., 2006. "A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 328-336.
    43. Costa, Rogério L. & Vasconcelos, G.L., 2003. "Long-range correlations and nonstationarity in the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 231-248.
    44. Zoltan Eisler & Janos Kertesz, 2004. "Multifractal model of asset returns with leverage effect," Papers cond-mat/0403767, arXiv.org, revised May 2004.
    45. R. L. Costa & G. L. Vasconcelos, 2003. "Long-range correlations and nonstationarity in the Brazilian stock market," Papers cond-mat/0302342, arXiv.org.
    46. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
    47. Ayadi, O. Felix & Pyun, C. S., 1994. "An application of variance ratio test to the Korean securities market," Journal of Banking & Finance, Elsevier, vol. 18(4), pages 643-658, September.
    48. Cheung, Yin-Wong & Lai, Kon S., 1995. "A search for long memory in international stock market returns," Journal of International Money and Finance, Elsevier, vol. 14(4), pages 597-615, August.
    49. Jorge L. Urrutia, 1995. "Tests Of Random Walk And Market Efficiency For Latin American Emerging Equity Markets," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 18(3), pages 299-309, September.
    50. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
    51. L. Kullmann & J. Kertesz & K. Kaski, 2002. "Time dependent cross correlations between different stock returns: A directed network of influence," Papers cond-mat/0203256, arXiv.org, revised May 2002.
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