Testing for detailed balance in a financial market

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.