上证指数高频数据的多重分形错觉

以上证指数5分钟取样的高频数据为例,采用配分函数法对每一交易日的数据进行多重分形分析,发现质量指数τ(q)为线性函数.用统计自举生成随机时间序列以深入剖析多重分形谱f(α),发现约有51%的交易日,其多重分形特性无法通过显著性检验.进一步分析发现,所有真实时间序列的奇异性强度与随机序列的奇异性强度相差无几,因而完全可以用后者加以解释.因此,上证指数本身并不具多重分形特性.

Illusionary multifractality in high-frequency data of Shanghai Stock Exchange Composite Index

Multifractal analysis of the intraday five-minute high-frequency data of Shanghai Stock Exchange Composite (SSEC) was conducted by utilizing the partition function method,resulting in linear mass exponent functions τ(q) .Shuffled series generated by bootstrapping were used to perform a careful scrutiny on the extracted multifractal spectra f(α).It is found that the multifractal features in about 51% trading days are statistically insignificant.Moreover,the singularity strength of the real data is indistinguishable from that of the shuffled data and the latter can be used to account for the former.Hence,the so-called multifractality claimed for the SSEC (and other prices or indexes) is merely an illusion.