Regularity Analysis of Inter-Out-of-Equilibrium State Intervals in Financial Markets

The inter-out-of-equilibrium state interval is analyzed in order to detect determinism in financial markets. We divide the time series of the return for price increments into two phases, equilibrium and out-of-equilibrium phases, due to two phase phenomena. Using an attractor reconstructed from a singular time series via Takens' theorem, the nonlinearity and determinism of inter-out-of-equilibrium state intervals are closely examined. Assuming an extended integrate-and-fire model analogous to fractional Brownian motion, a one-to-one correspondence is identified between the underlying system states and the reconstructed inter-out-of-equilibrium state interval vectors of a certain dimension. As compared to typical models driven by deterministic or stochastic processes, the inter-out-of-equilibrium state interval in the financial markets is found to exhibit features similar to stochastic properties.