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Estimating the Algorithmic Complexity of Stock Markets

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  • Olivier Brandouy
  • Jean-Paul Delahaye
  • Lin Ma

Abstract

Randomness and regularities in Finance are usually treated in probabilistic terms. In this paper, we develop a completely different approach in using a non-probabilistic framework based on the algorithmic information theory initially developed by Kolmogorov (1965). We present some elements of this theory and show why it is particularly relevant to Finance, and potentially to other sub-fields of Economics as well. We develop a generic method to estimate the Kolmogorov complexity of numeric series. This approach is based on an iterative "regularity erasing procedure" implemented to use lossless compression algorithms on financial data. Examples are provided with both simulated and real-world financial time series. The contributions of this article are twofold. The first one is methodological : we show that some structural regularities, invisible with classical statistical tests, can be detected by this algorithmic method. The second one consists in illustrations on the daily Dow-Jones Index suggesting that beyond several well-known regularities, hidden structure may in this index remain to be identified.

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  • Olivier Brandouy & Jean-Paul Delahaye & Lin Ma, 2015. "Estimating the Algorithmic Complexity of Stock Markets," Papers 1504.04296, arXiv.org.
    • Handle: RePEc:arx:papers:1504.04296
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    References listed on IDEAS

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    1. Hector Zenil & Jean‐Paul Delahaye, 2011. "An Algorithmic Information Theoretic Approach To The Behaviour Of Financial Markets," Journal of Economic Surveys, Wiley Blackwell, vol. 25(3), pages 431-463, July.
    2. Jean-Paul Delahaye & Hector Zenil, 2011. "An algorithmic information-theoretic approach to the behaviour of financial markets," Post-Print hal-00825528, HAL.
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    4. Giglio, Ricardo & Matsushita, Raul & Figueiredo, Annibal & Gleria, Iram & Da Silva, Sergio, 2008. "Algorithmic complexity theory and the relative efficiency of financial markets," MPRA Paper 8704, University Library of Munich, Germany.
    5. repec:ebl:ecbull:v:7:y:2008:i:6:p:1-12 is not listed on IDEAS
    6. Andreia Dionisio & Rui Menezes & Diana A. Mendes, 2007. "Entropy and Uncertainty Analysis in Financial Markets," Papers 0709.0668, arXiv.org.
    7. Lo, Melody & Lee, Cheng-Few, 2006. "A reexamination of the market efficiency hypothesis: Evidence from an electronic intra-day, inter-dealer FX market," The Quarterly Review of Economics and Finance, Elsevier, vol. 46(4), pages 565-585, September.
    8. Armin Shmilovici & Yael Alon-Brimer & Shmuel Hauser, 2003. "Using a Stochastic Complexity Measure to Check the Efficient Market Hypothesis," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 273-284, October.
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    Cited by:

    1. Krongthong Khairiree & Chonnart Meenanun, 2015. "Students? Project-Based Learning: Local Commercial Products and Marketing Mix," Proceedings of International Academic Conferences 2604495, International Institute of Social and Economic Sciences.

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