摘要翻译：
为了研究多个时间序列中的时滞互相关，我们提出了一种改进的时滞随机矩阵理论。我们将该方法应用于48个世界指数，每个指数适用于48个不同的国家。我们在量化风险的收益绝对值中发现了长程幂律互相关，并发现它们比收益之间的互相关衰减得慢得多。对于国际投资经理来说，这种相互关联的程度构成了“坏消息”，他们可能认为通过在各国进行多样化投资可以降低风险。我们发现，当市场冲击在全球范围内传播时，风险衰减非常缓慢。我们通过引入一个全局因子模型(GFM)来解释这些时滞互相关，在该模型中，所有指数收益都随着单个全局因子的变化而波动。对于每一对单个时间序列的收益，收益（或幅度）之间的互相关可以用全局因子收益（或幅度）的自相关来建模。我们用主成分分析来估计全局因子，在去除全局趋势后，使残差的方差最小。利用随机矩阵理论，可以用全局因子来解释世界指数的相当大一部分互相关，从而支持GFM的实用性。我们演示了GFM在世界范围内预测风险，以及在寻找不相关的单个指数方面的应用。我们发现10个指数实际上与全球因子无关，与其余的世界指数无关，这是世界经理人降低投资组合风险的相关信息。最后，我们认为，这种通用方法可以应用于从地震学、生理学到大气地球物理等广泛的时间序列测量现象。
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英文标题：
《Quantifying and Modeling Long-Range Cross-Correlations in Multiple Time
  Series with Applications to World Stock Indices》
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作者：
Duan Wang, Boris Podobnik, Davor Horvati\'c, and H.Eugene Stanley
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最新提交年份：
2011
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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：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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英文摘要：
  We propose a modified time lag random matrix theory in order to study time lag cross-correlations in multiple time series. We apply the method to 48 world indices, one for each of 48 different countries. We find long-range power-law cross-correlations in the absolute values of returns that quantify risk, and find that they decay much more slowly than cross-correlations between the returns. The magnitude of the cross-correlations constitute "bad news" for international investment managers who may believe that risk is reduced by diversifying across countries. We find that when a market shock is transmitted around the world, the risk decays very slowly. We explain these time lag cross-correlations by introducing a global factor model (GFM) in which all index returns fluctuate in response to a single global factor. For each pair of individual time series of returns, the cross-correlations between returns (or magnitudes) can be modeled with the auto-correlations of the global factor returns (or magnitudes). We estimate the global factor using principal component analysis, which minimizes the variance of the residuals after removing the global trend. Using random matrix theory, a significant fraction of the world index cross-correlations can be explained by the global factor, which supports the utility of the GFM. We demonstrate applications of the GFM in forecasting risks at the world level, and in finding uncorrelated individual indices. We find 10 indices are practically uncorrelated with the global factor and with the remainder of the world indices, which is relevant information for world managers in reducing their portfolio risk. Finally, we argue that this general method can be applied to a wide range of phenomena in which time series are measured, ranging from seismology and physiology to atmospheric geophysics.
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PDF链接：
https://arxiv.org/pdf/1102.2240