Volatility behavior of visibility graph EMD financial time series from Ising interacting system

• A financial price model is developed and investigated by stochastic Ising system.
• Empirical mode decomposition is used to decompose financial data into different frequency series.
• Volatility behavior of returns for financial time series is studied by visibility graph and horizontal visibility graph.
• Complexity analysis is performed for the considered series.
• Statistical analysis illustrates that the simulation data could exhibit the similar properties as the real data.

A financial market dynamics model is developed and investigated by stochastic Ising system, where the Ising model is the most popular ferromagnetic model in statistical physics systems. Applying two graph based analysis and multiscale entropy method, we investigate and compare the statistical volatility behavior of return time series and the corresponding IMF series derived from the empirical mode decomposition (EMD) method. And the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, we find that the degree distribution of visibility graph for the simulation series has the power law tails, and the assortative network exhibits the mixing pattern property. All these features are in agreement with the real market data, the research confirms that the financial model established by the Ising system is reasonable.