Scale invariant distribution and multifractality of volatility multipliers in stock markets

The statistical properties of the multipliers of the absolute returns are investigated using one-minute high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale, providing direct evidence of the existence of scale invariance in financial data. The multipliers with base a = 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a. We unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers, that is, the values of s and a.