具有长时记忆的时变方差的推广模型

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摘要翻译：
ARCH过程(R.F.Engle，1982)构成了随机时间序列的范型生成器，其方差与时间相关，就像它出现在除了ARCH诞生的经济学之外的广泛系统中一样。尽管ARCH过程捕捉到了所谓的“波动聚类”和随机变量的渐近幂律概率密度分布，但它不能再现许多这些时间序列的进一步统计特性，如：以Hurst指数的大值(H>0.8)为特征的瞬时方差的强持久性，以及绝对值自相关函数的渐近幂律衰减。通过考虑从具有q指数形式的过去回报的相关中得到的有效回报，我们能够修正原始模型的局限性。此外，这种改进可以通过正确选择唯一的附加参数$q_{m}$来实现。通过模拟SP500财务指数的日波动，对其有效性和实用性进行了评价。
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英文标题：
《On a generalised model for time-dependent variance with long-term memory》
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作者：
Silvio M. Duarte Queiros
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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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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英文摘要：
  The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law probability density distribution of the random variable, it is not capable to reproduce further statistical properties of many of these time series such as: the strong persistence of the instantaneous variance characterised by large values of the Hurst exponent (H > 0.8), and asymptotic power-law decay of the absolute values self-correlation function. By means of considering an effective return obtained from a correlation of past returns that has a q-exponential form we are able to fix the limitations of the original model. Moreover, this improvement can be obtained through the correct choice of a sole additional parameter, $q_{m}$. The assessment of its validity and usefulness is made by mimicking daily fluctuations of SP500 financial index.
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PDF链接：
https://arxiv.org/pdf/0705.3248

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关键词：distribution Econophysics Fluctuations Quantitative Applications values Hurst 模拟 幂律 相关