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Estimating fractal dimension using stable distributions and exploring long memory through ARFIMA models in Athens Stock Exchange

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  • Epaminondas Panas
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    Abstract

    It is argued that the study of the correct specification of returns distributions has attractive implications in financial economics. This study estimates Levy-stable (fractal) distributions that can accurately account for skewness, kurtosis, and fat tails. The Levy-stable family distributions are parametrized by the Levy index (α), 0 < (α), ≤ 2, and include the normal distribution as a special case (α = 2). The Levy index, α, is the fractal dimension of the probability space. The unique feature of Levy-stable family distributions is the existence of a relationship between the fractal dimension of the probability space andthe fractal dimensionof the time series. This relationshipis simply expressed in terms of Hurst exponent (H), i.e. α = 1/ H. In addition, Hurst exponent is related to long-memory effects. Thus, estimating the Levy index allows us to determine long-memory effects. The immediate practical implication of the present work is that on the one hand we estimate the shape of returns distributions and on the other hand we investigate the fractal dimensions. Overall, then, the Levy-stable family distributions methodology appears to be useful for analysing the returns distribution, for understanding the fractal dimension of returns and for providing the researcher with direct insights into the long-memory effects of stock returns. A second approach to test the long memory hypothesis is attempted in this paper. This test involves an estimation of the ARFIMA models. A comparative analysis of the two approaches indicates the existence of long-memory in the Athens Stock Exchange. The results of this study are based on a sample of stocks from the Athens Stock Exchange using daily data.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Financial Economics.

    Volume (Year): 11 (2001)
    Issue (Month): 4 ()
    Pages: 395-402

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    Handle: RePEc:taf:apfiec:v:11:y:2001:i:4:p:395-402

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    Cited by:
    1. Kian-Ping Lim & Melvin J. Hinich, 2005. "Cross-temporal universality of non-linear dependencies in Asian stock markets," Economics Bulletin, AccessEcon, vol. 7(1), pages 1-6.
    2. Ladislav Kristoufek & Miloslav Vosvrda, 2012. "Measuring capital market efficiency: Global and local correlations structure," Papers 1208.1298, arXiv.org.
    3. Yuan, Ying & Zhuang, Xin-tian & Liu, Zhi-ying, 2012. "Price–volume multifractal analysis and its application in Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3484-3495.
    4. Hull, Matthew & McGroarty, Frank, 2014. "Do emerging markets become more efficient as they develop? Long memory persistence in equity indices," Emerging Markets Review, Elsevier, vol. 18(C), pages 45-61.
    5. Cajueiro, Daniel O. & Gogas, Periklis & Tabak, Benjamin M., 2009. "Does financial market liberalization increase the degree of market efficiency? The case of the Athens stock exchange," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 50-57, March.
    6. Turvey, Calum G., 2007. "A note on scaled variance ratio estimation of the Hurst exponent with application to agricultural commodity prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 155-165.
    7. Alvarez-Ramirez, Jose & Rodriguez, Eduardo & Espinosa-Paredes, Gilberto, 2012. "Is the US stock market becoming weakly efficient over time? Evidence from 80-year-long data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5643-5647.
    8. Bariviera, Aurelio Fernández, 2011. "The influence of liquidity on informational efficiency: The case of the Thai Stock Market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4426-4432.
    9. Lin, Xiaoqiang & Fei, Fangyu, 2013. "Long memory revisit in Chinese stock markets: Based on GARCH-class models and multiscale analysis," Economic Modelling, Elsevier, vol. 31(C), pages 265-275.
    10. repec:ebl:ecbull:v:7:y:2003:i:3:p:1-13 is not listed on IDEAS
    11. Jussi Tolvi, 2003. "Long memory in a small stock market," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-13.
    12. Abounoori, Esmaiel & Shahrazi, Mahdi & Rasekhi, Saeed, 2012. "An investigation of Forex market efficiency based on detrended fluctuation analysis: A case study for Iran," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3170-3179.
    13. DiSario, Robert & Saraoglu, Hakan & McCarthy, Joseph & Li, Hsi, 2008. "Long memory in the volatility of an emerging equity market: The case of Turkey," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(4), pages 305-312, October.
    14. Sánchez Granero, M.A. & Trinidad Segovia, J.E. & García Pérez, J., 2008. "Some comments on Hurst exponent and the long memory processes on capital markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5543-5551.
    15. Epaminondas Panas & Vassilia Ninni, 2010. "The Distribution of London Metal Exchange Prices: A Test of the Fractal Market Hypothesis," European Research Studies Journal, European Research Studies Journal, vol. 0(2), pages 192-210.
    16. repec:ebl:ecbull:v:7:y:2005:i:1:p:1-6 is not listed on IDEAS

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