基于MF-DFA的中国股指期货价格的多重分形实证研究

本文通过应用多重分形谱分析法和多重分形消除趋势波动分析（MF-DFA）法，研究了新产生的中国股指期货市场的多重分形性。通过对2942个股指期货最后十分钟结算价格的分析，我们发现中国股指期货的收益率具有长程相关性和多重分形性，期货价格波动并不能用单一的标度指数进行充分描述。进一步通过将原始序列和转换后的收益序列进行比较，转换过程包括重排以及相位随机化，我们发现导致中国股指期货市场多重分形性的两种不同成因。研究结果表明，虽然厚尾分布是造成多重分形性的一个方面，但长程相关性才是引起中国股指期货市场多重分形的主要原因。

Empirical Analysis of the Chinese Stock Index Futures Price Based on Multifractal Detrended Fluctuation

Based on the multifractal spectrum analysis and multifractal detrended fluctuation analysis （MF-DFA）, this paper empirically studies the multifractal properties of the Chinese stock index futures market. We find that the Chinese stock index futures returns exhibit long-range correlations and multifractality by using a total of 2942 ten-minute closing prices, making the single-scale index insufficient to describe the futures price fluctuations. Further, we show the existence of two different sources of the multifractality for the Chinese stock index futures market by comparing the original time series with the transformed time series through shuffling procedure and phase randomization procedure. Our results suggest that the multifractality is mainly due to long-range correlations, although the fat-tailed probability distributions also contribute to such multifractal behavior.