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摘要翻译：
Baldovin和Stella最近从时间尺度的非均匀性和连续价格收益之间的线性解相关出发，提出了一种建立金融指数时间演化模型的方法。我们首先用学生分布代替幂律截断L\'evy分布使其完全显式化；我们还证明了该模型的解析可处理性扩展到更大一类对称广义双曲分布，并给出了其多元特征函数的完整计算；更一般地说，在这个框架中产生的随机过程可以表示为Wiener过程的混合。Baldovin和Stella模型虽然很好地模拟了波动松弛现象，如Omori定律，但未能再现其他程式化的事实，如杠杆效应或一些时间反转不对称。我们讨论了如何修改这一过程的动力学，以便更准确地再现真实数据。
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英文标题：
《The Ups and Downs of Modeling Financial Time Series with Wiener Process
Mixtures》
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作者：
Damien Challet and Pier Paolo Peirano
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最新提交年份：
2009
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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：Physics 物理学
二级分类：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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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：
Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated L\'evy distributions; we also show that the analytic tractability of the model extends to the larger class of symmetric generalized hyperbolic distributions and provide a full computation of their multivariate characteristic functions; more generally, the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The Baldovin and Stella model, while mimicking well volatility relaxation phenomena such as the Omori law, fails to reproduce other stylized facts such as the leverage effect or some time reversal asymmetries. We discuss how to modify the dynamics of this process in order to reproduce real data more accurately.
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PDF链接：
https://arxiv.org/pdf/0807.4163
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