摘要翻译：
我们分析了应用于平稳增量过程的滑动窗口时间平均是否收敛到概率极限的问题。问题集中在通过增量x(t，t)=x(t+t)-x(t)的时间平均值构造的平均值、相关性和密度上，并且假设增量是独立于t分布的。我们证明了将切比雪夫定理应用于平稳增量函数的时间平均的条件是强烈违反的。我们认为，对于平稳增量和非平稳增量，Tchebyshev定理提供了从单个历史时间序列构造emsemble平均值和密度的基础，如果序列在平均值上表现出一定的统计周期性，就像在外汇市场中一样。
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英文标题：
《Time vs. Ensemble Averages for Nonstationary Time Series》
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作者：
Joseph L. McCauley
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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：Other Condensed Matter        其他凝聚态物质
分类描述：Work in condensed matter that does not fit into the other cond-mat classifications
在不适合其他cond-mat分类的凝聚态物质中工作
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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：
  We analyze the question whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the increment x(t,T)=x(t+T)-x(t)and the assumption is that the increment is distributed independently of t. We show that the condition for applying Tchebyshev's Theorem to time averages of functions of stationary increments is strongly violated. We argue that, for both stationary and nonstationary increments, Tchebyshev's Theorem provides the basis for constructing emsemble averages and densities from a single, historic time series if, as in FX markets, the series shows a definite statistical periodicity on the average.
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PDF链接：
https://arxiv.org/pdf/0804.0902