摘要翻译：
我们试图在一般二次自回归(QARCH)模型的背景下揭示波动反馈效应的精细结构，该模型假设今天的波动率可以表示为过去日收益率的一般二次型。当二次核为对角线时，恢复标准的ARCH或GARCH框架。这些模型对美国股票收益的校准揭示了几个意想不到的特征。二次核的非对角（非拱）系数在样本内和样本外都非常显著，但所有这些系数都比对角元素小一个数量级。这证实了每日收益在波动反馈机制中扮演着特殊的角色，正如ARCH模型所假设的那样。反馈核表现出令人惊讶的复杂结构，与文献中提出的模型不相容。它的光谱特性表明过去回报的波动中性模式的存在。发现二次核的对角线部分以滞后的幂律衰减，符合波动的长记忆性。最后，QARCH模型提出了金融时间序列中一些违反时间反转对称性的现象，这些现象确实在经验中被观察到，尽管振幅比预测的要小得多。我们推测，一个忠实的波动率模型应该包含ARCH反馈效应和一个随机成分。
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英文标题：
《The fine-structure of volatility feedback I: multi-scale
  self-reflexivity》
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作者：
R\'emy Chicheportiche and Jean-Philippe Bouchaud
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最新提交年份：
2013
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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：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
  We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily returns. The standard ARCH or GARCH framework is recovered when the quadratic kernel is diagonal. The calibration of these models on US stock returns reveals several unexpected features. The off-diagonal (non ARCH) coefficients of the quadratic kernel are found to be highly significant both In-Sample and Out-of-Sample, but all these coefficients turn out to be one order of magnitude smaller than the diagonal elements. This confirms that daily returns play a special role in the volatility feedback mechanism, as postulated by ARCH models. The feedback kernel exhibits a surprisingly complex structure, incompatible with models proposed so far in the literature. Its spectral properties suggest the existence of volatility-neutral patterns of past returns. The diagonal part of the quadratic kernel is found to decay as a power-law of the lag, in line with the long-memory of volatility. Finally, QARCH models suggest some violations of Time Reversal Symmetry in financial time series, which are indeed observed empirically, although of much smaller amplitude than predicted. We speculate that a faithful volatility model should include both ARCH feedback effects and a stochastic component.
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PDF链接：
https://arxiv.org/pdf/1206.2153