摘要翻译:
我们回顾了将正负阶分数阶导数算子应用于标准随机游动所产生的模型的统计性质,并证明所产生的随机游动显示出缓慢衰减的自相关函数。讨论了这些相关步态与计量经济学研究中常用的分数积分自回归(FIGARCH)模型之间的关系。研究了相关随机游动模拟经验金融时间序列的应用,并与FIGARCH和更简单的FIARCH过程的预测结果进行了比较。并与经验数据进行了比较。
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英文标题:
《Fractional derivatives of random walks: Time series with long-time
memory》
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作者:
H. Eduardo Roman and Markus Porto
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最新提交年份:
2008
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分类信息:
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: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:
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-known fractionally integrated autoregressive (FIGARCH) models, commonly used in econometric studies, is discussed. The application of correlated random walks to simulate empirical financial times series is considered and compared with the predictions from FIGARCH and the simpler FIARCH processes. A comparison with empirical data is performed.
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PDF链接:
https://arxiv.org/pdf/0806.3171