Centro de Física do Porto, Porto, Portugal.
PLoS One. 2011 Mar 31;6(3):e18149. doi: 10.1371/journal.pone.0018149.
We introduce a generalization 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 . 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 characterized by large values of the Hurst exponent (H>0.8), which are ubiquitous features in complex systems.
我们介绍了一种广为人知的 ARCH 过程的推广，该过程广泛用于生成无相关性的随机时间序列，这些序列具有长期的非高斯分布和在（瞬时）标准差中表现出聚类特征的持久相关性。具体来说，受到这样一个事实的启发，即在各种系统中，影响事件几乎不会被遗忘，我们将这个过程分为两个不同的阶段：第一个阶段是在一段时间内平均波动低于某个阈值 的正常时期，另一个阶段是当局部标准差超过 时。在前一种情况下，我们使用异方差过程的标准规则，而在后一种情况下，系统开始回忆超过阈值的过去值。我们的结果表明，对于适当的参数值，该模型能够提供长尾概率密度函数和瞬时方差的强持续性，其特征是赫斯特指数（H>0.8）的值较大，这是复杂系统中普遍存在的特征。
