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摘要翻译：
定量金融的一个核心问题是建立资产价格时间演变的概率模型，从而能够可靠地预测其未来的波动性。就像在一些自然现象中一样，这样一个模型的预测必须与我们记录中单个过程实现的数据进行比较。为了使这种比较具有统计意义，不能避免从单个历史时间序列中提取的某些量的平稳性假设，例如在给定时间间隔内的收益分布。这种假设带来了掩盖或歪曲基本过程的非平稳性的风险，并对其相关性作出了不正确的说明。在这里，我们克服了这一困难，展示了纽约市场开盘后约三小时内欧元/美国兑美元的五年每日交易记录，提供了足够丰富的历史集合。这个集合的统计数据允许提出和检验驱动汇率的随机过程的适当模型。这是一个非马尔可夫的，自相似的过程，具有非平稳的回报。该模型是基于时间非均匀的反常标度服从回报分布而构造的，经验系综相关器与模型的预测是一致的。
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英文标题：
《Modeling the non-Markovian, non-stationary scaling dynamics of financial
markets》
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作者：
Fulvio Baldovin, Dario Bovina, Francesco Camana, and Attilio L. Stella
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最新提交年份：
2010
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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：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
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英文摘要：
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such a model must be compared with the data of a single process realization in our records. In order to give statistical significance to such a comparison, assumptions of stationarity for some quantities extracted from the single historical time series, like the distribution of the returns over a given time interval, cannot be avoided. Such assumptions entail the risk of masking or misrepresenting non-stationarities of the underlying process, and of giving an incorrect account of its correlations. Here we overcome this difficulty by showing that five years of daily Euro/US-Dollar trading records in the about three hours following the New York market opening, provide a rich enough ensemble of histories. The statistics of this ensemble allows to propose and test an adequate model of the stochastic process driving the exchange rate. This turns out to be a non-Markovian, self-similar process with non-stationary returns. The empirical ensemble correlators are in agreement with the predictions of this model, which is constructed on the basis of the time-inhomogeneous, anomalous scaling obeyed by the return distribution.
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PDF链接：
https://arxiv.org/pdf/0909.3244
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