Statistical tests of distributional scaling properties for financial return series
提出了一套正式的统计检验方法，用于判断金融收益率序列的分布标度性质最符合哪类分形过程，并通过蒙特卡洛模拟和日内股指与汇率数据验证了其有效性。
Existing empirical evidence of distributional scaling in financial returns has helped motivate the use of multifractal processes for modelling return processes. However, this evidence has relied on informal tests that may be unable to reliably distinguish multifractal processes from other related classes. The current paper develops a formal statistical testing procedure for determining which class of fractal process is most consistent with the distributional scaling properties in a given sample of data. Our testing methodology consists of a set of test statistics, together with a model-based bootstrap resampling scheme to obtain sample p-values. We demonstrate in Monte Carlo exercises that the proposed testing methodology performs well in a wide range of testing environments relevant for financial applications. Finally, the methodology is applied to study the scaling properties of a data-set of intraday equity index and exchange rate returns. The empirical results suggest that the scaling properties of these return series may be inconsistent with purely multifractal processes.