Multifractal properties of price change and volume change of stock market indices

We study auto-correlations and cross-correlations of daily price changes and daily volume changes of thirteen global stock market indices, using multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DXA). We find rather distinct multifractal behavior of price and volume changes. Our results indicate that the time series of price changes are more complex than those of volume changes, and that large fluctuations dominate multifractal behavior of price changes, while small fluctuations dominate multifractal behavior of volume changes. We also find that there is an absence of correlations in price changes, there are anti-persistent long-term correlations in volume changes, and there are anti-persistent long-term cross-correlations between price and volume changes. Shuffling the series reveals that multifractality of both price changes and volume changes arises from a broad probability density function.