Persistence of return distribution sequence in financial markets

The analysis of return distribution is an important topic in risk management and investment practice. This study analyzes time -varying distribution sequences and characterizes persistence with topological correlation coefficients (TCC), where the distribution consists of cross-sectional returns. We used some models to show that TCC can effectively analyze persistence, and found that both the autocorrelation structure and volatility clustering of time series can lead to the persistence of the distribution sequence. We analyzed the persistence of the return distribution sequences in the Chinese market and the US market. The calculation shows that some sequences have significant persistence. In addition, we analyzed factors that affect the persistence, where model -based analysis provides a baseline for comparison. The analysis shows that neither autocorrelation structure nor volatility clustering can fully explain persistence, so the generation mechanism of persistence is complex. In particular, dynamic analysis shows that persistence is time -varying and that there are significant differences between the two markets. This study provides a way to study distribution sequences, which can help analyze the predictability of distributions.