Multifractal and recurrence behaviors of continuum percolation-based financial price dynamics

Abstract

The modeling of financial price fluctuations is always a hot research aspect that many researchers are concerned about. A financial price model based on two-dimensional continuum percolation system, which is one of the most important statistical physics systems, is introduced in this work. In the model, the fluctuations of stock price changes are assumed to be attributed to the market information interactions among the traders, and the percolation cluster is taken to represent the traders holding the same investment attitude. Then, multifractal detrended fluctuation analysis method is adopted to study the multifractal behaviors of simulation data with different parameter sets. Finally, the recurrence plot and recurrence quantification analysis techniques are applied to investigate the complex determinism dynamics hidden in the simulated stock returns from the price model, as well as in their different intrinsic mode functions (IMFs) decomposed from the empirical mode decomposition method. Abundant and distinctive recurrence behaviors can be observed among returns and IMFs time series. In the meanwhile, the corresponding behaviors of the Chinese Shanghai Composite Index is studied for comparison.