金融市场中基于互信息率的网络

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英文标题：
《Mutual Information Rate-Based Networks in Financial Markets》
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作者：
Pawe{\\l} Fiedor
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最新提交年份：
2014
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英文摘要：
  In the last years efforts in econophysics have been shifted to study how network theory can facilitate understanding of complex financial markets. Main part of these efforts is the study of correlation-based hierarchical networks. This is somewhat surprising as the underlying assumptions of research looking at financial markets is that they behave chaotically. In fact it\'s common for econophysicists to estimate maximal Lyapunov exponent for log returns of a given financial asset to confirm that prices behave chaotically. Chaotic behaviour is only displayed by dynamical systems which are either non-linear or infinite-dimensional. Therefore it seems that non-linearity is an important part of financial markets, which is proved by numerous studies confirming financial markets display significant non-linear behaviour, yet network theory is used to study them using almost exclusively correlations and partial correlations, which are inherently dealing with linear dependencies only. In this paper we introduce a way to incorporate non-linear dynamics and dependencies into hierarchical networks to study financial markets using mutual information and its dynamical extension: the mutual information rate. We estimate it using multidimensional Lempel-Ziv complexity and then convert it into an Euclidean metric in order to find appropriate topological structure of networks modelling financial markets. We show that this approach leads to different results than correlation-based approach used in most studies, on the basis of 15 biggest companies listed on Warsaw Stock Exchange in the period of 2009-2012 and 91 companies listed on NYSE100 between 2003 and 2013, using minimal spanning trees and planar maximally filtered graphs.
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中文摘要：
在过去的几年里，经济物理学的研究已经转向研究网络理论如何促进对复杂金融市场的理解。这些工作的主要部分是研究基于相关性的分层网络。这有点令人惊讶，因为研究金融市场的基本假设是，它们的行为是混乱的。事实上，经济物理学家通常会估计给定金融资产对数收益的最大李雅普诺夫指数，以确认价格的行为是无序的。混沌行为只表现为非线性或无限维的动力系统。因此，非线性似乎是金融市场的一个重要组成部分，许多研究证实了这一点，金融市场表现出显著的非线性行为，但网络理论被用来研究它们，几乎完全使用相关性和偏相关性，它们本质上只处理线性依赖关系。在本文中，我们介绍了一种将非线性动力学和依赖性纳入层次网络的方法，以利用互信息及其动态扩展来研究金融市场：互信息率。我们使用多维Lempel-Ziv复杂性对其进行估计，然后将其转换为欧几里德度量，以便找到金融市场建模网络的适当拓扑结构。基于2009-2012年在华沙证券交易所上市的15家最大公司和2003-2013年在纽约证券交易所100家上市的91家公司，我们使用最小生成树和平面最大过滤图，表明这种方法与大多数研究中使用的基于相关性的方法得出的结果不同。
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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：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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关键词：金融市场 互信息 Experimental Econophysics correlations