Estimating the Algorithmic Complexity of Stock Markets

21 Pages Posted: 12 May 2011  

Olivier Brandouy

French National Center for Scientific Research (CNRS) - Groupe de Recherche en Économie Théorique et Appliquée (GREThA)

J. P. Delahaye

affiliation not provided to SSRN

L. Ma

affiliation not provided to SSRN

Date Written: May 1, 2011

Abstract

Randomness and regularities in finance are usually treated in probabilistic terms. In this paper, we develop a different approach in using a non-probabilistic framework based on the algorithmic information theory initially developed by Kolmogorov (1965). We develop a generic method to estimate the Kolmogorov complexity of numeric series. This approach is based on an iterative “regularity erasing procedure” (REP) implemented to use lossless compression algorithms on financial data. The REP is found to be necessary to detect hidden structures, as one should “wash out” well-established financial patterns (i.e. stylized facts) to prevent algorithmic tools from concentrating on these non-profitable patterns. The main contribution of this article is methodological: we show that some structural regularities, invisible with classical statistical tests, can be detected by this algorithmic method. Our final illustration on the daily Dow-Jones Index reveals a weak compression rate, once well- known regularities are removed from the raw data. This result could be associated to a high efficiency level of the New York Stock Exchange, although more effective algorithmic tools could improve this compression rate on detecting new structures in the future.

Suggested Citation

Brandouy, Olivier and Delahaye, J. P. and Ma, L., Estimating the Algorithmic Complexity of Stock Markets (May 1, 2011). International Conference of the French Finance Association (AFFI), May 11-13, 2011; Algorithmic Finance 2015, 4:3-4, 159-178. Available at SSRN: https://ssrn.com/abstract=1836886 or http://dx.doi.org/10.2139/ssrn.1836886

Olivier Brandouy (Contact Author)

French National Center for Scientific Research (CNRS) - Groupe de Recherche en Économie Théorique et Appliquée (GREThA) ( email )

Avenue Léon Duguit
Aveneu Duguit
Pessac, 33 608
France

J. P. Delahaye

affiliation not provided to SSRN

L. Ma

affiliation not provided to SSRN

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