摘要翻译：
对数正态连续随机级联是一类已成功应用于各个领域的多重分形过程。研究了与该模型有关的几个统计问题。我们首先对它们的主要性质做了一个快速但广泛的回顾，并表明这些性质中的大多数可以用解析的方法研究。然后，我们在小间歇度λ2ll1$范围内，即当多重分形度很小时，建立了这些过程的近似理论。这使得我们可以证明与这些过程相关的概率分布具有一些随时间尺度变化的非常简单的聚集性质。这种控制过程在不同时间尺度上的性质，使我们能够解决参数估计问题。我们表明，人们必须区分两种不同的渐近状态：第一种被称为“低频状态”，对应于取一个总体尺寸增加的样本，而第二种被称为“高频状态”，对应于以增加的采样率对过程进行采样。我们证明，第一种情形导致了收敛的估计量，而在高频情形下，情况要复杂得多：只有间歇系数λ2$可以用一致估计量估计。然而，我们表明，在实际情况下，人们可以检测渐近区域的性质（低频与高频），从而决定其他参数的估计是否可靠。最后，我们说明了我们在参数估计和聚集性质方面的结果，使我们能够成功地将这些模型用于金融时间序列的建模和预测。
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英文标题：
《Log-Normal continuous cascades: aggregation properties and estimation.
  Application to financial time-series》
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作者：
E. Bacry, A. Kozhemyak and J.-F. Muzy
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最新提交年份：
2008
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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：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：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
  Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review of their main properties and show that most of these properties can be analytically studied. We then develop an approximation theory of these processes in the limit of small intermittency $\lambda^2\ll 1$, i.e., when the degree of multifractality is small. This allows us to prove that the probability distributions associated with these processes possess some very simple aggregation properties accross time scales. Such a control of the process properties at different time scales, allows us to address the problem of parameter estimation. We show that one has to distinguish two different asymptotic regimes: the first one, referred to as the ''low frequency regime'', corresponds to taking a sample whose overall size increases whereas the second one, referred to as the ''high frequency regime'', corresponds to sampling the process at an increasing sampling rate. We show that, the first regime leads to convergent estimators whereas, in the high frequency regime, the situation is much more intricate : only the intermittency coefficient $\lambda^2$ can be estimated using a consistent estimator. However, we show that, in practical situations, one can detect the nature of the asymptotic regime (low frequency versus high frequency) and consequently decide whether the estimations of the other parameters are reliable or not. We finally illustrate how both our results on parameter estimation and on aggregation properties, allow one to successfully use these models for modelization and prediction of financial time series.
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PDF链接：
https://arxiv.org/pdf/0804.0185