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Long-term stochastic dependence in financial prices: evidence from the German stock market

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  • Thomas Lux

Abstract

A number of authors have argued that financial prices may exhibit hidden long-term dependence. We consider this claim analysing German stock market data. Applying three different concepts for the identification of long memory effects, virtually no evidence of such behaviour is found for stock market returns. Another recent assertion says that long term memory may not be pertinent to stock returns but rather to the conditional volatility of financial market prices. As it turns out, this claim is very much supported by our investigation of German stock market data. Furthermore, the long memory property is more pronounced in absolute values of returns than in the squares of returns (both used as proxies for volatility). The methods employed are: the time-honoured procedure of estimating the Hurst exponent for the scaling behaviour of the range of cumulative departures from the mean of a time series, the modified range analysis.

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  • Thomas Lux, 1996. "Long-term stochastic dependence in financial prices: evidence from the German stock market," Applied Economics Letters, Taylor & Francis Journals, vol. 3(11), pages 701-706.
    • Handle: RePEc:taf:apeclt:v:3:y:1996:i:11:p:701-706
    DOI: 10.1080/135048596355691
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    1. Siew Ann Cheong, 2013. "Econophysics: An Experimental Course for Advanced Undergraduates in the Nanyang Technological University," IIM Kozhikode Society & Management Review, , vol. 2(2), pages 79-99, July.
    2. Lux, Thomas & Morales-Arias, Leonardo, 2010. "Forecasting volatility under fractality, regime-switching, long memory and student-t innovations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2676-2692, November.
    3. Lux, Thomas & Morales-Arias, Leonardo, 2010. "Relative forecasting performance of volatility models: Monte Carlo evidence," Kiel Working Papers 1582, Kiel Institute for the World Economy (IfW Kiel).
    4. Alexander Subbotin, 2008. "A multi-horizon scale for volatility," Post-Print halshs-00261514, HAL.
    5. Tan, Pei P. & Galagedera, Don U.A. & Maharaj, Elizabeth A., 2012. "A wavelet based investigation of long memory in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2330-2341.
    6. Rivera-Castro, Miguel A. & Miranda, José G.V. & Cajueiro, Daniel O. & Andrade, Roberto F.S., 2012. "Detecting switching points using asymmetric detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 170-179.
    7. Rafal Weron, 2001. "Measuring long-range dependence in electricity prices," Papers cond-mat/0103621, arXiv.org.
    8. Thomas Lux, 2003. "The Multi-Fractal Model of Asset Returns:Its Estimation via GMM and Its Use for Volatility Forecasting," Computing in Economics and Finance 2003 14, Society for Computational Economics.
    9. C. Chiarella & X-Z. He, 2001. "Asset price and wealth dynamics under heterogeneous expectations," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 509-526.
    10. Tripathy, Naliniprava, 2022. "Long memory and volatility persistence across BRICS stock markets," Research in International Business and Finance, Elsevier, vol. 63(C).
    11. Gomes, Luís M. P. & Soares, Vasco J. S. & Gama, Sílvio M. A. & Matos, José A. O., 2018. "Long-term memory in Euronext stock indexes returns: an econophysics approach," Business and Economic Horizons (BEH), Prague Development Center, vol. 14(4), pages 862-881, August.
    12. Dominique, C-Rene & Rivera-Solis, Luis Eduardo, 2012. "The dynamics of market share’s growth and competition in quadratic mappings," MPRA Paper 43652, University Library of Munich, Germany.
    13. Liu, Ruipeng & Lux, Thomas, 2010. "Flexible and robust modelling of volatility comovements: a comparison of two multifractal models," Kiel Working Papers 1594, Kiel Institute for the World Economy (IfW Kiel).
    14. Dominique, C-Rene & Rivera-Solis, Luis Eduardo, 2012. "Short-term Dependence in Time Series as an Index of Complexity: Example from the S&P-500 Index," MPRA Paper 41408, University Library of Munich, Germany.
    15. Sanjay Rajagopal & Patrick Hays, 2012. "Return Persistence in the Indian Real Estate Market," International Real Estate Review, Global Social Science Institute, vol. 15(3), pages 283-305.
    16. Lux, Thomas & Morales-Arias, Leonardo, 2009. "Forecasting volatility under fractality, regime-switching, long memory and student-t innovations," Kiel Working Papers 1532, Kiel Institute for the World Economy (IfW Kiel).
    17. Lux, Thomas & Morales-Arias, Leonardo & Sattarhoff, Cristina, 2011. "A Markov-switching multifractal approach to forecasting realized volatility," Kiel Working Papers 1737, Kiel Institute for the World Economy (IfW Kiel).
    18. Zunino, Luciano & Figliola, Alejandra & Tabak, Benjamin M. & Pérez, Darío G. & Garavaglia, Mario & Rosso, Osvaldo A., 2009. "Multifractal structure in Latin-American market indices," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2331-2340.
    19. Sensoy, Ahmet & Tabak, Benjamin M., 2015. "Time-varying long term memory in the European Union stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 147-158.
    20. Mejra Festic & Alenka Kavkler & Silvo Dajcman, 2012. "Long memory in the Croatian and Hungarian stock market returns," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics and Business, vol. 30(1), pages 115-139.
    21. Dominique, C-René & Rivera-Solis, Luis Eduardo, 2011. "Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index," MPRA Paper 34860, University Library of Munich, Germany.
    22. Mensi, Walid & Tiwari, Aviral Kumar & Al-Yahyaee, Khamis Hamed, 2019. "An analysis of the weak form efficiency, multifractality and long memory of global, regional and European stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 72(C), pages 168-177.
    23. Bhandari, Avishek, 2020. "Long memory and fractality among global equity markets: A multivariate wavelet approach," MPRA Paper 99653, University Library of Munich, Germany.
    24. A. Sensoy & Benjamin M. Tabak, 2013. "How much random does European Union walk? A time-varying long memory analysis," Working Papers Series 342, Central Bank of Brazil, Research Department.

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