摘要翻译：
基于反重整化群策略的思想，提出并讨论了一个金融资产动态随机模型。在此策略下，我们构造了基于集合概率密度随时间变化的多元初等收益分布。在其最简单的版本中，该模型是一个内生的自回归成分和一个随机的重新标度因子的产物，该因子也被设计来体现外生的影响。可以证明增量的平稳性和遍历性等数学性质。由于参数数目相对较少，模型校正可以方便地基于矩量法，如S&P500指数的历史数据。校正后的模型很好地解释了许多程式化的事实，如波动率聚类、波动率自相关函数的幂律衰减、聚集收益分布随时间的多尺度变化等。与金融领域的经验证据一致，在时间反转下，动态不是不变的，通过适当的概括，收益分布的偏态和杠杆效应可以包括在内。该模型的分析可处理性为应用打开了有趣的视角，例如在获得衍生品定价的封闭公式方面。进一步的重要特征是：在一定范围内与金融中广泛使用的自回归模型联系的可能性；部分解决波动性的长记忆和短记忆成分的可能性，并在应用于历史序列时得到一致的结果。
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英文标题：
《Scaling symmetry, renormalization, and time series modeling》
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作者：
Marco Zamparo, Fulvio Baldovin, Michele Caraglio, Attilio L. Stella
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最新提交年份：
2013
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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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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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英文摘要：
  We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous auto-regressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance in terms of obtaining closed formulas for derivative pricing. Further important features are: The possibility of making contact, in certain limits, with auto-regressive models widely used in finance; The possibility of partially resolving the long-memory and short-memory components of the volatility, with consistent results when applied to historical series.
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PDF链接：
https://arxiv.org/pdf/1305.3243