英文标题：
《Self-affinity in financial asset returns》
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作者：
John Goddard, Enrico Onali
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最新提交年份：
2014
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英文摘要：
  We test for departures from normal and independent and identically distributed (NIID) returns, when returns under the alternative hypothesis are self-affine. Self-affine returns are either fractionally integrated and long-range dependent, or drawn randomly from an L-stable distribution with infinite higher-order moments. The finite sample performance of estimators of the two forms of self-affinity is explored in a simulation study which demonstrates that, unlike rescaled range analysis and other conventional estimation methods, the variant of fluctuation analysis that considers finite sample moments only is able to identify either form of self-affinity. However, when returns are self-affine and long-range dependent under the alternative hypothesis, rescaled range analysis has greater power than fluctuation analysis. The finite-sample properties of the estimators when returns exhibit either form of self-affinity can be exploited to determine the source of self-affinity in empirical returns data. The techniques are illustrated by means of an analysis of the fractal properties of the daily logarithmic returns for the indices of 11 stock markets.
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中文摘要：
当替代假设下的收益是自仿射的时，我们检验是否偏离正态和独立同分布（NIID）收益。自仿射收益要么是分数积分的、长期相关的，要么是从具有无限高阶矩的L-稳定分布中随机抽取的。在一项模拟研究中探讨了两种形式的自相似性估计量的有限样本性能，该研究表明，与重标极差分析和其他传统估计方法不同，只考虑有限样本矩的波动分析变体能够识别任何一种形式的自相似性。然而，在替代假设下，当收益率是自仿射的且与长期相关时，重标极差分析比波动分析更有效。当收益表现出任何一种形式的自相似性时，估计量的有限样本性质可以用来确定经验收益数据中的自相似性来源。通过分析11个股票市场指数的日对数收益率的分形特性，说明了这些技术。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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