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分形市场理论从动力学和几何学的角度探讨金融系统的复杂非线性特征,突破传统金融整数维的概念引入了分数维,成为研究金融市场特征的有效分析工具。本文运用多重分形消除趋势波动分析方法(MF-DFA),对上海和新加坡的燃料油价格序列进行多重分形特征对比分析,研究发现燃料油价格收益率不符合传统金融理论的随机游走特征,市场具有显著的长期记忆性,广义Hurst指数随波动函数的阶数变化而变化;燃料油期货市场不是一个有效资本市场,并不遵循传统的随机游走特征,是一个典型的多重分形市场。此外,多重分形谱研究表明上海燃料油期货市场的多重分形谱更宽,其分形波动特征更显著,不能采用单一标度指标描述。
Fractal market theory explores the complex nonlinear characteristics of financial system from the perspective of dynamics and geometry, breaks the traditional concept of financial integral dimension and introduces fractal dimension, which becomes an effective analytical tool for studying the characteristics of financial market. In this paper, MF-DFA is used to analyze the multifractal characteristics of fuel oil prices in Shanghai and Singapore. It is found that the price-earnings ratio of fuel oil does not accord with the random walk characteristics of traditional financial theory. Has a significant long-term memory, the general Hurst index changes with the order of the fluctuation function; fuel oil futures market is not an effective capital market, does not follow the traditional characteristics of random walk, is a typical multifractal market. In addition, the study of multifractal spectrum shows that the multifractal spectrum of Shanghai fuel oil futures market is broader and its fractal fluctuation characteristics are more remarkable, which can not be described by a single scale index.