Multivariate out-of-sample tests for Granger causality

A time series is said to Granger cause another series if it has incremental predictive power when forecasting it. While Granger causality tests have been studied extensively in the univariate setting, much less is known for the multivariate case. Multivariate out-of-sample tests for Granger causality are proposed and their performance is measured by a simulation study. The results are graphically represented by size-power plots. It emerges that the multivariate regression test is the most powerful among the considered possibilities. As a real data application, it is investigated whether the consumer confidence index Granger causes retail sales in Germany, France, the Netherlands and Belgium.     

Causality analysis of neural connectivity: New tool and limitations of spectral Granger causality

Granger causality (GC) is one of the most popular measures to reveal causality influence of time series based on the estimated linear regression model and has been widely applied in economics and neuroscience due to its simplicity, understandability and easy implementation. Especially, its counterpart in frequency domain, spectral GC, has recently received growing attention to study causal interactions of neurophysiological data in different frequency ranges. In this paper, on the one hand, for one equality in the linear regression model (frequency domain) we point out that all items at the right-hand side of the equality make contributions (thus have causal influence) to the unique item at the left-hand side of the equality, and thus a reasonable definition for causality from one variable to another variable (i.e., the unique item) should be able to describe what percentage the variable occupies among all these contributions. Along this line, we propose a new spectral causality definition. On the other hand, we point out that spectral GC has its inherent limitations because of the use of the transfer function of the linear regression model and as a result may not reveal real causality at all and lead to misinterpretation result. By one example we demonstrate that the results of spectral GC analysis are misleading but the results from our definition are much reasonable. So, our new tool may have wide potential applications in neuroscience.     

运用偏相关因果分析推断神经网络的真实结构

自从格兰杰提出因果关系的概念之后,格兰杰因果关系在构造神经网络的结构方面的应用越来越广泛,因为它可以得到神经网络的一个有向图。对于只有两个神经元的神经元网络,可以用通常的格兰杰因果关系去分析它们谁是因,谁是果。对于三个神经元以上的神经网络,由于神经元之间存在间接的作用,就不能象对两个神经元直接运用格兰杰因果关系去研究它们之间的结构了,而要用偏相关因果关系进行分析。论文介绍了偏相关因果关系的基本概念,并对一个模拟的三个神经元的网络比较了格兰杰因果关系和偏相关因果关系的区别。     

矢量格兰杰因果关系及其在复杂网络中的应用

自从格兰杰1969年提出因果关系的概念之后,格兰杰因果关系在构造生物网络(基因网络、蛋白质网络、神经网络)的结构方面的应用越来越广泛,但是它只能用于研究单个节点和单个节点之间的内在联系。而实际的生物网络由于基因、神经元等的相互作用,往往呈现出非常复杂的网络结构,需要研究网络节点构成的组与组之间的内在联系。将格兰杰因果关系进行推广,得到矢量格兰杰因果关系的研究方法,并通过两个模拟的例子验证了方法的有效性。     

频域格兰杰因果关系及其在信号处理中的应用

自从格兰杰1969年提出因果关系的概念之后,格兰杰因果关系在信号处理、计算神经科学等许多领域的应用越来越广。人们可以利用格兰杰因果关系来分析多个变量之间的直接的相互作用,从而进一步研究各类变量之间的内在联系。以往都是在时域空间进行分析的,也就是说分析的对象都是时间序列数据,研究这些变量之间随着时间的变化是如何联系的。在时域空间的基础上,进一步从频域空间上对变量进行研究,分析在哪个频率段上变量之间存在相互作用,所得到的结论当然更具有意义。     

Root cause diagnosis of plant-wide oscillations using Granger causality

Oscillations are common in closed-loop controlled processes which, once generated, can propagate along process flows and feedback paths of the whole plant. It is important to detect and diagnose such oscillations to maintain high control performance. This paper presents a new data-driven time series method for diagnosing the sources and propagation paths of plant-wide oscillations. The proposed method first uses a latent variable method to select features which carry significant common oscillations, then applies both time-domain Granger causality and spectral Granger causality to provide reliable diagnosis of oscillation sources and propagations. Simulation tests and an industrial case study are shown to demonstrate the effectiveness of the proposed method.     

Predicting software defects with causality tests

In this paper, we propose a defect prediction approach centered on more robust evidences towards causality between source code metrics (as predictors) and the occurrence of defects. More specifically, we rely on the Granger causality test to evaluate whether past variations in source code metrics values can be used to forecast changes in time series of defects. Our approach triggers alarms when changes made to the source code of a target system have a high chance of producing defects. We evaluated our approach in several life stages of four Java-based systems. We reached an average precision greater than 50% in three out of the four systems we evaluated. Moreover, by comparing our approach with baselines that are not based on causality tests, it achieved a better precision.     

非线性格兰杰因果关系在计算神经科学的应用

自从格兰杰1969年提出因果关系的概念之后,格兰杰因果关系的应用越来越广泛,但都是用来分析线性时间序列数据之间的内在联系。将线性格兰杰因果关系推广到非线性的情形,首先利用核函数的方法建立非线性时间序列模型,再按照线性格兰杰因果关系的基本思想定义非线性格兰杰因果关系,最后通过一个模拟的例子验证该方法的有效性。模拟数据的结果表明,该方法能有效地分析非线性数据之间的内在联系。     

Unbalance estimation using linear and nonlinear regression

This paper considers the problem of unbalance estimation of rotating machinery. It is formulated as a parameter estimation problem, where the unknowns enter nonlinearly in a regression model. By use of a certain method, the problem can be reformulated as a linear estimation procedure with a closed form solution. This procedure is sometimes known as the influence coefficient method. In its derivation, no special treatment is devoted to disturbing terms and imperfections in the model. Therefore, a novel method is derived which takes disturbances into account, leading to a nonlinear estimator.The two procedures are compared and analyzed with respect to their statistical accuracy. Using the example of unbalance estimation of a separator, the nonlinear approach is shown to give superior performance.     

Observability functions for linear and nonlinear systems

A generalization of the zero-state observability function is considered for nonlinear systems. The linear time-invariant case is considered as an application in model reduction problems.     

Granger 相关性与时间序列预测

提出一种将Granger相关信息用于时间序列预测的方法,以解决时间序列预测过程中信息利用不完全的问题.首先,通过Granger相关性检验确定时间序列系统中的可利用信息;然后,利用神经网络将可利用信息抽取出来;最后,将抽取的可利用信息融入到时间序列的预测中.实验结果验证了所提出预测方法的有效性和稳定性.     

Spurious Granger causality between a broken-trend stationary process and a stochastic trend process

This paper examines spurious Granger causality between a trend stationary process with structural breaks and a stochastic trend process. Monte Carlo simulations show that whether or not there are deterministic variables in the testing models, the sample size and the parameter values of the data generation process can affect the empirical frequencies of spurious Granger causality relations in different degrees. The analysis also points out that an alternative rank-based causality test method can avoid the risk of spurious causality to some extent by adopting an intercept and deterministic trend term in the testing regressions.     

On system gains for linear and nonlinear systems

System gains, and bounds for system gains, are determined for stable linear and nonlinear systems in different signal setups which include ℓ_p signal setups and certain persistent signal generalizations of the ℓ₂ and ℓ₁ signal setups. These results show that robust H_∞ and ℓ₁ control generalize to very versatile persistent signal settings. Relationships between different system gains are also derived. Finally, an application of nonlinear system gain bounds is given by establishing induced ℓ_∞ modelling error bounds for a class of (generalized) piecewise linear systems approximated with simpler linear time-invariant models.     

Determination of ECoG information flow activity based on Granger causality and Hilbert transformation

Analysis of directional information flow patterns among different regions of the brain is important for investigating the relation between ECoG (electrocorticographic) and mental activity. The objective is to study and evaluate the information flow activity at different frequencies in the primary motor cortex. We employed Granger causality for capturing the future state of the propagation path and direction between recording electrode sites on the cerebral cortex. A grid covered the right motor cortex completely due to its size (approx. 8 cm × 8 cm) but grid area extends to the surrounding cortex areas. During the experiment, a subject was asked to imagine performing two activities: movement of the left small finger and/or movement of the tongue. The time series of the electrical brain activity was recorded during these trials using an 8 × 8 (0.016–300 Hz band with) ECoG platinum electrode grid, which was placed on the contralateral (right) motor cortex. For detection of information flow activity and communication frequencies among the electrodes, we have proposed a method based on following steps: (i) calculation of analytical time series such as amplitude and phase difference acquired from Hilbert transformation, (ii) selection of frequency having highest interdependence for the electrode pairs for the concerned time series over a sliding window in which we assumed time series were stationary, (iii) calculation of Granger causality values for each pair with selected frequency. The information flow (causal influence) activity and communication frequencies between the electrodes in grid were determined and shown successfully. It is supposed that information flow activity and communication frequencies between the electrodes in the grid are approximately the same for the same pattern. The successful employment of Granger causality and Hilbert transformation for the detection of the propagation path and direction of each component of ECoG among different sub-cortex areas were capable of determining the information flow (causal influence) activity and communication frequencies between the populations of neurons successfully.     

Ultimate boundedness control of linear systems with band-bounded nonlinear actuators and additive measurement noise

For linear systems driven by band-bounded nonlinear actuators, a set of linear matrix inequality (LMI) based sufficient conditions are derived for finding state feedback controllers which assure ultimate boundedness of state trajectories. Besides actuator nonlinearity, it is assumed that additive noise exists when state variables are measured for feedback. The purpose is to minimize the ultimate boundedness region while tolerating noise of the largest magnitude. When a state feedback controller is determined for a given system by solving the LMI conditions or by any other means, a less conservative LMI condition is given for further examination of the resultant ultimate boundedness region and tolerable noise magnitude.     

On linear models for nonlinear systems

Best linear time-invariant (LTI) approximations are analysed for several interesting classes of discrete nonlinear time-invariant systems. These include nonlinear finite impulse response systems and a class of nonsmooth systems called bi-gain systems. The Fréchet derivative of a smooth nonlinear system is studied as a potential good LTI model candidate. The Fréchet derivative is determined for nonlinear finite memory systems and for a class of Wiener systems. Most of the concrete results are derived in an ?_∞ signal setting. Applications to linear controller design, to identification of linear models and to estimation of the size of the unmodelled dynamics are discussed.     

多元时间序列因果关系分析研究综述

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.     

Measuring causality between collaborative and individual gaze metrics for collaborative problem-solving with intelligent tutoring systems

When students are working collaboratively and communicating verbally in a technology-enhanced environment, the system cannot track what collaboration is happening outside of the technology, making it difficult to fully assess the collaboration of the students and adapt accordingly. In this article, we propose using gaze measures as a proxy for cognitive processes to achieve collaboration awareness. Specifically, we use Granger causality to analyse the causal relationships between collaborative and individual gaze measures from students working on a fractions intelligent tutoring system and the influence that the students' dialogue, prior knowledge, or success has on these relationships. We found that collaborative gaze patterns drive the individual focus in the pairs with high posttest scores and when they are engaged in problem-solving dialogues but the opposite with low performing students. Our work adds to the literature by extending the correlational relationships between individual and collaborative gaze measures to causal relationships and suggests indicators that can be used within an adaptive system.