摘要翻译：
我们介绍了众所周知的ARCH过程的一个推广，该过程被广泛用于产生不相关的随机时间序列，这些随机时间序列具有长期非高斯分布和在（瞬时）标准差中表现出聚类分布的长期相关性。具体地说，受影响事件很难被遗忘的各种系统的启发，我们将这一过程分为两个不同的机制：第一个机制适用于规则周期，即某一时间段内波动的平均波动率低于某一阈值；另一个机制则是当局部标准差大于该阈值时。在前一种情况下，我们对异方差过程使用标准规则，而在后一种情况下，系统开始回忆超过阈值的过去值。结果表明，在适当的参数取值下，该模型能够提供胖尾概率密度函数，并且以Hurst指数大于0.8为特征的瞬时方差具有强持久性，这是复杂系统中普遍存在的特征。
---
英文标题：
《Minding impacting events in a model of stochastic variance》
---
作者：
Silvio M. Duarte Queiros, Evaldo M. F. Curado, Fernando D. Nobre
---
最新提交年份：
2011
---
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
--
一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--
一级分类：Physics        物理学
二级分类：Computational Physics        计算物理学
分类描述：All aspects of computational science applied to physics.
应用于物理学的计算科学的各个方面。
--

---
英文摘要：
  We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold and another one when the local standard deviation outnumbers it. In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterised by large values of the Hurst exponent is greater than 0.8, which are ubiquitous features in complex systems.
---
PDF链接：
https://arxiv.org/pdf/1102.4819