摘要翻译：
本文对马德里证券交易所IBEX35指数的高频收益进行了统计分析。我们发现它的概率分布在不同的时间尺度上似乎是稳定的，这是在许多不同的金融时间序列中观察到的一个程式化的事实。然而，使用极大似然估计和不同的拟合优度检验对数据的深入分析拒绝了L\'Evy-稳定定律作为一个似乎可信的潜在概率模型。分析表明，正态逆高斯分布比广义双曲分布族中的任何一个子类都更适合于数据，当然也比L\'eVy-稳定律更好。此外，分布的右（左）尾似乎遵循幂律，指数\alpha=4.60(\alpha=4.28)。最后，我们给出了观测到的稳定性是由于数据的时间相关性或非平稳性所致的证据。
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英文标题：
《Scaling, stability and distribution of the high-frequency returns of the
  IBEX35 index》
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作者：
Pablo Su\'arez-Garc\'ia, David G\'omez-Ullate
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最新提交年份：
2012
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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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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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英文摘要：
  In this paper we perform a statistical analysis of the high-frequency returns of the IBEX35 Madrid stock exchange index. We find that its probability distribution seems to be stable over different time scales, a stylized fact observed in many different financial time series. However, an in-depth analysis of the data using maximum likelihood estimation and different goodness-of-fit tests rejects the L\'evy-stable law as a plausible underlying probabilistic model. The analysis shows that the Normal Inverse Gaussian distribution provides an overall fit for the data better than any of the other subclasses of the family of the Generalized Hyperbolic distributions and certainly much better than the L\'evy-stable laws. Furthermore, the right (resp. left) tail of the distribution seems to follow a power-law with exponent \alpha=4.60 (resp. \alpha =4.28). Finally, we present evidence that the observed stability is due to temporal correlations or non-stationarities of the data.
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PDF链接：
https://arxiv.org/pdf/1208.0317