摘要翻译：
回归分析中的协整方法是基于增量平稳的假设。具有固定时滞的平稳增量称为积分I(d)。Granger发现了一类回归模型，其中协整起作用，并产生了标准经济学中均衡预期所需的遍历行为。金融市场折损收益是鞅，且鞅不满足回归方程。我们扩展了标准讨论，以发现标准回归模型之外满足积分I(d)的减损过程类。在计量经济学的语言中，感兴趣的模型是单位根模型，即鞅。典型的鞅没有固定增量，那些固定增量一般不承认遍历性。我们的分析使我们对前面观察到的外汇汇率和相对价格水平之间缺乏均衡做出评论。
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英文标题：
《Integration I(d) of Nonstationary Time Series: Stationary and
  nonstationary increments》
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作者：
Joseph L. McCauley, Kevin E. Bassler, and Gemunu H. Gunaratne
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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：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：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：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：
  The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior required for equilibrium expectations in standard economics. Detrended finance market returns are martingales, and martingales do not satisfy regression equations. We extend the standard discussion to discover the class of detrended processes beyond standard regression models that satisfy integration I(d). In the language of econometrics, the models of interest are unit root models, meaning martingales. Typical martingales do not have stationary increments, and those that do generally do not admit ergodicity. Our analysis leads us to comment on the lack of equilibrium observed earlier between FX rates and relative price levels.
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PDF链接：
https://arxiv.org/pdf/0803.3959