Nonlinear continuous fluctuation intensity financial dynamics and complexity behavior.

The exploration of return volatility dynamics is of great significance to evaluate investment risk, avoid stock market crisis, and purchase stock portfolio. In this paper, we propose a novel concept to characterize the fluctuation duration of stock markets, which is continuous fluctuation intensity (CFI). The CFI represents the duration for continuous increasing or decreasing return volatilities (or normalized absolute returns) above or below a previous day's value. Distinguished from previous studies, the CFI does not need to set a threshold in advance but to select the sequence of return volatilities that are continuously growing or falling in the series. So, the research on continuous fluctuation intensity is a new approach in return volatility study. For investigating the nonlinear properties of CFI, probability distribution, autocorrelation analysis, and scatterplot analysis are utilized for the empirical data from China and USA stock markets. Besides, fractional sample entropy and fuzzy entropy are employed to explore the complexity of CFI series. Then, some meaningful results of CFI series are acquired, which manifest that the study of the proposed concept is feasible and valuable. Moreover, we do the same investigations for return volatility series to explore the similarities and differences between CFI series and volatility series.