多元时间序列因果关系分析研究综述

任伟杰; 韩敏

doi:10.16383/j.aas.c180189

多元时间序列因果关系分析研究综述

doi: 10.16383/j.aas.c180189

任伟杰^{1, 2,},
韩敏^{1, 2,}

1.
大连理工大学电子信息与电气工程学部大连 116023
2.
大连理工大学工业装备智能控制与优化教育部重点实验室大连 116023

基金项目: 国家自然科学基金(61773087), 中央高校基本科研业务费(DUT18RC(6)005)资助

详细信息

作者简介:
任伟杰：大连理工大学电子信息与电气工程学部博士研究生. 主要研究方向为时间序列分析和特征选择.E-mail: renweijie@mail.dlut.edu.cn

韩敏：大连理工大学电子信息与电气工程学部教授. 主要研究方向为模式识别, 复杂系统建模及时间序列预测. 本文通信作者.E-mail: minhan@dlut.edu.cn

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出版历程
- 收稿日期: 2018-04-02
- 录用日期: 2018-11-22
- 网络出版日期: 2021-01-29
- 刊出日期: 2021-01-29

Survey on Causality Analysis of Multivariate Time Series

REN Wei-Jie^{1, 2
,},
HAN Min^{1, 2
,}

1.
Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116023
2.
Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian 116023

Funds: Supported by National Natural Science Foundation of China (61773087) and Fundamental Research Funds for the Central Universities (DUT18RC(6)005)

摘要

摘要:
多元时间序列的因果关系分析是数据挖掘领域的研究热点. 时间序列数据包含着与时间动态有关的、未知的、有价值的信息, 因此若能挖掘出这些知识进而对时间序列未来趋势进行预测或干预, 具有重要的现实意义. 为此, 本文综述了多元时间序列因果关系分析的研究进展、应用与展望. 首先, 本文归纳了主要的因果分析方法, 包括Granger因果关系分析、基于信息理论的因果分析和基于状态空间的因果分析; 然后, 总结了不同方法的优缺点、适用范围和发展方向, 并概述了其在不同领域的典型应用; 最后, 讨论了多元时间序列因果分析方法待解决的问题和未来研究趋势.
- 多元时间序列 /
- Granger因果分析 /
- 转移熵 /
- 状态空间
Abstract:
The causality analysis of multivariate time series is a research hotspot in data mining. Time series data contains unknown, valuable information related to temporal dynamics. Therefore, it is of great practical significance to be able to mine these knowledge and then predict or intervene the future trend of time series. For this reason, this paper reviews the research progress, application and prospects of causality analysis of multivariate time series. Firstly, this paper summarizes the main causality analysis methods, including Granger causality analysis, causality analysis based on information theory and causality analysis based on state space. Then, we summarize the advantages and disadvantages, scope of application and development directions of different methods, and outline their typical applications in different fields. Finally, the problems to be solved and future research trends of the causality analysis methods of multivariate time series are discussed.
- Multivariate time series /
- Granger causality analysis /
- transfer entropy /
- state space

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图 1 收敛交叉映射基本原理示意图

Fig. 1 Schematic diagram of the basic principle of convergence cross mapping

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表 1 Granger因果关系分析及其改进方法

Table 1 Granger causality analysis and its improvement methods

类别	研究者	发表年份	方法名称	文献
Granger因果模型	Granger	1969	Granger 因果指数 (GCI)	[15]
条件Granger因果模型	Geweke	1982	条件 Granger 因果指数 (CGCI)	[23]
	Chen 等	2004	条件扩展 Granger 因果指数 (CEGCI)	[24]
	Siggiridou 等	2016	限制条件 Granger 因果指数 (RCGCI)	[25]
Lasso-Granger因果模型	Arnold 等	2007	Lasso-Granger 因果模型	[26]
	Shojaie 等	2010	截断 Lasso-Granger 因果模型	[27]
	Bolstad 等	2011	Grouped-Lasso-Granger 因果模型	[28]
	Yang 等	2017	Grouped-Lasso 非线性条件 Granger 因果模型	[29]
非线性Granger因果模型	Ancona 等	2004	RBF-Granger 因果模型	[30]
	Marinazzo 等	2008	Kernel-Granger 因果模型	[31-32]
	Wu 等	2011	KCCA-Granger 因果模型	[33]
	Hu 等	2014	Copula-Granger 因果模型	[34]
	Montalto 等	2015	NN-Granger 因果模型	[35]
频域Granger因果模型	Geweke	1982	Spectral-Granger 因果模型	[23]
	Baccalá 等	2001	偏定向相干性 (PDC)	[36]
	Kamiński 等	2001	直接传递函数 (DTF)	[37]

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表 2 基于信息理论的因果关系分析方法

Table 2 Causality analysis methods based on information theory

类别	研究者	发表年份	方法名称	文献
转移熵	Schreiber	2000	转移熵 (TE)	[40]
	Staniek 等	2008	符号转移熵 (STE)	[42]
	Kugiumtzis	2013	偏符号转移熵 (PSTE)	[43]
条件熵	Faes 等	2011	条件熵 (CE)	[44]
条件互信息	Frenzel 等	2007	偏互信息 (PMI)	[45]
条件互信息	Kugiumtzis	2013	基于混合嵌入的偏互信息 (PMIME)	[46]

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表 3 因果分析方法应用范围比较

Table 3 Comparison of application range of causality analysis methods

研究者	方法名称	非线性	多变量	非平稳	文献
Granger	Granger 因果指数				[15]
Geweke	条件 Granger 因果指数		√		[23]
Chen 等	条件扩展 Granger 因果指数	√	√		[24]
Siggiridou 等	限制条件 Granger 因果指数	√	√		[25]
Arnold 等	Lasso-Granger 因果模型		√		[26]
Shojaie 等	截断 Lasso-Granger 因果模型		√		[27]
Bolstad 等	Grouped-Lasso-Granger 因果模型		√		[28]
Yang 等	Grouped-Lasso 非线性条件 Granger 因果模型	√	√		[29]
Ancona 等	RBF-Granger 因果模型	√			[30]
Marinazzo 等	Kernel-Granger 因果模型	√	√		[31-32]
Wu 等	KCCA-Granger 因果模型	√	√		[33]
Hu 等	Copula-Granger 因果模型	√	√		[34]
Montalto 等	NN-Granger 因果模型	√	√		[35]
Geweke	Spectral-Granger 因果模型		√		[23]
Baccalá 等	偏定向相干性		√		[36]
Kamiński 等	直接传递函数		√		[37]
Schreiber	转移熵	√			[40]
Staniek 等	符号转移熵	√		√	[42]
Kugiumtzis	偏符号转移熵	√	√	√	[43]
Faes 等	条件熵	√	√		[44]
Frenzel 等	偏互信息	√	√		[45]
Kugiumtzis	基于混合嵌入的偏互信息	√	√		[46]
Arnhold 等	非线性相互依赖指标 S 和 H	√			[61]
Quiroga 等	非线性相互依赖指标 N	√			[62]
Andrzejak 等	非线性相互依赖指标 M	√			[63]
Chicharro 等	非线性相互依赖指标 L	√		√	[64]
Sugihara 等	收敛交叉映射	√			[65]

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