股票指数的多重分形性：事实还是虚构？
Multifractality in stock indexes: Fact or fiction?
摘要：
对4个股票市场指数（包括恒生指数、深证成指、标普500指数和纳斯达克指数）在单个交易日内的日内数据进行多重分形分析和广泛的统计检验，以检验指数（而不是收益率）是否具有多重分形性。我们发现，质量指数$τ(q)$是线性的和奇异性$α(q)$是接近1的所有交易日和所有指数。此外，我们发现了强有力的证据表明，原始数据集的标度行为不能区分从那些混洗时间序列。因此，股票市场指数的多重分形性只是一种假象。
英文摘要：
Multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes (including HSI, SZSC, S&P500, and NASDAQ) to check whether the indexes (instead of the returns) possess multifractality. We find that the mass exponent $τ(q)$ is linear and the singularity $α(q)$ is close to 1 for all trading days and all indexes. Furthermore, we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of the shuffled time series. Hence, the so-called multifractality in the intraday stock market indexes is merely an illusion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
