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On the non-stationarity of financial time series: impact on optimal portfolio selection

Author

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  • Giacomo Livan
  • Jun-ichi Inoue
  • Enrico Scalas

Abstract

We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence against the well-established common knowledge that using longer price time series provides better, more accurate, correlation estimates. Then, we investigate the possible consequences of instabilities in empirical correlation coefficient measurements on optimal portfolio selection. We rely on previously published works which provide a framework allowing to take into account possible risk underestimations due to the non-optimality of the portfolio weights being used in order to distinguish such non-optimality effects from risk underestimations genuinely due to non-stationarities. We interpret such results in terms of instabilities in some spectral properties of portfolio correlation matrices.

Suggested Citation

  • Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers 1205.0877, arXiv.org, revised Jul 2012.
  • Handle: RePEc:arx:papers:1205.0877
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    File URL: http://arxiv.org/pdf/1205.0877
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    References listed on IDEAS

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    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
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    3. G. Livan & S. Alfarano & E. Scalas, 2011. "The fine structure of spectral properties for random correlation matrices: an application to financial markets," Papers 1102.4076, arXiv.org.
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    7. Gabor Papp & Szilard Pafka & Maciej A. Nowak & Imre Kondor, 2005. "Random Matrix Filtering in Portfolio Optimization," Papers physics/0509235, arXiv.org.
    8. Michael C. Munnix & Takashi Shimada & Rudi Schafer & Francois Leyvraz Thomas H. Seligman & Thomas Guhr & H. E. Stanley, 2012. "Identifying States of a Financial Market," Papers 1202.1623, arXiv.org.
    9. Marsili, Matteo & Raffaelli, Giacomo & Ponsot, Benedicte, 2009. "Dynamic instability in generic model of multi-assets markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1170-1181, May.
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    12. Z. Burda & A. Görlich & J. Jurkiewicz & B. Wacław, 2006. "Correlated Wishart matrices and critical horizons," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 49(3), pages 319-323, February.
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    Cited by:

    1. Marian Gidea & Daniel Goldsmith & Yuri Katz & Pablo Roldan & Yonah Shmalo, 2018. "Topological recognition of critical transitions in time series of cryptocurrencies," Papers 1809.00695, arXiv.org.
    2. repec:eee:phsmap:v:490:y:2018:i:c:p:1211-1227 is not listed on IDEAS
    3. Bertram During & Nicos Georgiou & Enrico Scalas, 2016. "A stylized model for wealth distribution," Papers 1609.08978, arXiv.org.
    4. A. E. Biondo & A. Pluchino & A. Rapisarda & D. Helbing, 2013. "Are random trading strategies more successful than technical ones?," Papers 1303.4351, arXiv.org, revised Jul 2013.
    5. Matthias Raddant & Friedrich Wagner, 2016. "Phase transition in the S&P stock market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 11(2), pages 229-246, October.
    6. Nicol'o Musmeci & Tomaso Aste & Tiziana Di Matteo, 2016. "What does past correlation structure tell us about the future? An answer from network filtering," Papers 1605.08908, arXiv.org.
    7. Nicol'o Musmeci & Tomaso Aste & Tiziana Di Matteo, 2014. "Risk diversification: a study of persistence with a filtered correlation-network approach," Papers 1410.5621, arXiv.org.

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