The scaling properties of stock markets based on modified multiscale multifractal detrended fluctuation analysis

• Investigate the scaling structures in Chinese stock markets and US stock markets by performing modified MMA method.
• Focus on the distribution histograms of Hurst surface.
• Allow the assessment of more universal and subtle scaling characteristics.

Here we propose the new method DH-MMA, based on multiscale multifractal detrended fluctuation analysis(MMA), to investigate the scaling properties in stock markets. It is demonstrated that our approach can provide a more stable and faithful description of the scaling properties in comprehensive range rather than fixing the window length and slide length. It allows the assessment of more universal and subtle scaling characteristics. We illustrate DH-MMA by selecting power-law artificial data sets and six stock markets from US and China. The US stocks exhibit very strong multifractality for positive values of qq, however, the Chinese stocks show stronger multifractality for negative qq than positive qq. In general, the US stock markets show similar behaviors, but Chinese stock markets display distinguishing characteristics.