Price–volume multifractal analysis and its application in Chinese stock markets

An empirical research on Chinese stock markets is conducted using statistical tools. First, the multifractality of stock price return series, r i ( r i = ln ( P t + 1 ) − ln ( P t ) ) and trading volume variation series, v i ( v i = ln ( V t + 1 ) − ln ( V t ) ) is confirmed using multifractal detrended fluctuation analysis. Furthermore, a multifractal detrended cross-correlation analysis between stock price return and trading volume variation in Chinese stock markets is also conducted. It is shown that the cross relationship between them is also found to be multifractal. Second, the cross-correlation between stock price P i and trading volume V i is empirically studied using cross-correlation function and detrended cross-correlation analysis. It is found that both Shanghai stock market and Shenzhen stock market show pronounced long-range cross-correlations between stock price and trading volume. Third, a composite index R based on price and trading volume is introduced. Compared with stock price return series r i and trading volume variation series v i , R variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume. Finally, we analyze the multifractal characteristics of R variation series before and after three financial events in China (namely, Price Limits, Reform of Non-tradable Shares and financial crisis in 2008) in the whole period of sample to study the changes of stock market fluctuation and financial risk. It is found that the empirical results verified the validity of R .