Scaling features of price-volume cross correlation

Price without transaction makes no sense. Trading volume authenticates its corresponding price, so there exists mutual information and correlation between price and trading volume. We are curious about fractal features of this correlation and need to know how structures in different scales translate information. To explore the influence of investment size (trading volume), price-wise (gain/loss), and time-scale effects, we analyzed the price and trading volume and their coupling by applying the MF-DXA method. Our results imply that price, trading volume and price-volume coupling exhibit a power law and are also multifractal. Meanwhile, considering developed markets, the price-volume couplings are significantly negatively correlated. However, in emerging markets, price has less of a contribution in price-volume coupling. In emerging markets in comparison with the developed markets, trading volume and price are more independent.