Symbolic complexity of volatility duration and volatility difference component on voter financial dynamics

The nonlinear complexity of volatility duration and volatility difference component based on voter financial dynamics is investigated in this paper. The statistic - volatility difference component is first introduced in this work, in an attempt to study the volatility behaviors comprehensively. The maximum change rate series and the average change rate series (both derived from the volatility difference components) are employed to characterize the volatility duration properties of financial markets. Further, for the proposed series model and the proposed financial statistic series (which are transformed to symbolic sequences), the permutation Lempel-Ziv complexity, a novel complexity measure, is introduced to study the corresponding randomness and complexity behaviors. Besides, Zipf analysis is also applied to investigate the corresponding Zipf distributions of the proposed series. The empirical study shows the similar complexity behaviors of volatility between the proposed price model and the real stock markets, which exhibits that the proposed model is feasible to some extent.