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Testing for Detailed Balance in a Financial Market

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  • Rudolf Fiebig
  • David Musgrove

Abstract

We test a historical price time series in a financial market (the NASDAQ 100 index) for a statistical property known as detailed balance. The presence of detailed balance would imply that the market can be modeled by a stochastic process based on a Markov chain, thus leading to equilibrium. In economic terms, a positive outcome of the test would support the efficient market hypothesis, a cornerstone of neo-classical economic theory. In contrast to the usage in prevalent economic theory the term equilibrium here is tied to the returns, rather than the price time series. The test is based on an action functional $S$ constructed from the elements of the detailed balance condition and the historical data set, and then analyzing $S$ by means of simulated annealing. Checks are performed to verify the validity of the analysis method. We discuss the outcome of this analysis.

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  • Rudolf Fiebig & David Musgrove, 2014. "Testing for Detailed Balance in a Financial Market," Papers 1403.3584, arXiv.org.
    • Handle: RePEc:arx:papers:1403.3584
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    References listed on IDEAS

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    1. Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2010. "Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 107-116.
    2. Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2011. "Replicating financial market dynamics with a simple self-organized critical lattice model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3120-3135.
    3. McCauley,Joseph L., 2009. "Dynamics of Markets," Cambridge Books, Cambridge University Press, number 9780521429627.
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