Measurement of Linear Dependence and Feedback between Multiple Time Series

Geweke, John

doi:10.1080/01621459.1982.10477803

Cited by 1,583 publications

(1,496 citation statements)

References 7 publications

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“…When X t and Y t are independent, F X,Y = 0. When this total interdependence is non-zero, Geweke [23] showed that F X,Y can be decomposed into three components,…”

Section: Materials and Methods (A) Pairwise Analysismentioning

confidence: 99%

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Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Wen

Rangarajan

Ding

2013

Phil. Trans. R. Soc. A.

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Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.

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“…When X t and Y t are independent, F X,Y = 0. When this total interdependence is non-zero, Geweke [23] showed that F X,Y can be decomposed into three components,…”

Section: Materials and Methods (A) Pairwise Analysismentioning

confidence: 99%

“…Under general conditions, the spectral measures integrated over the frequency yield their timedomain counterparts [23],…”

Section: Materials and Methods (A) Pairwise Analysismentioning

confidence: 99%

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Wen

Rangarajan

Ding

2013

Phil. Trans. R. Soc. A.

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“…Geweke [13] was the first to propose a linear bivariate time-series approach assessing linear Granger causality (LGC) based on the prediction error variance of the time series associated with a statistical test for causality [12]. If process X 2 has no causal influence on process X 1 , then LGC X 2 →X 1 becomes close to zero, which means that the knowledge of past values of X 2 does not improve the prediction of X 1 , but if LGC Bassani et al [15] estimated the direct causal coupling by applying two GC approaches (the F-test and the Wald test) along the baroreflex in two anaesthesiological procedures.…”

Section: (I) Linear Methodsmentioning

confidence: 99%

Cardiovascular and cardiorespiratory coupling analyses: a review

Schulz

Adochiei

Edu

et al. 2013

Phil. Trans. R. Soc. A.

139

127

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Recently, methods have been developed to analyse couplings in dynamic systems. In the field of medical analysis of complex cardiovascular and cardiorespiratory systems, there is growing interest in how insights may be gained into the interaction between regulatory mechanisms in healthy and diseased persons. The couplings within and between these systems can be linear or nonlinear. However, the complex mechanisms involved in cardiovascular and cardiorespiratory regulation very likely interact with each other in a nonlinear way. Recent advances in nonlinear dynamics and information theory have allowed the multivariate study of information transfer between time series. They therefore might be able to provide additional diagnostic and prognostic information in medicine and might, in particular, be able to complement traditional linear coupling analysis techniques. In this review, we describe the approaches (Granger causality, nonlinear prediction, entropy, symbolization, phase synchronization) most commonly applied to detect direct and indirect couplings between time series, especially focusing on nonlinear approaches. We will discuss their capacity to quantify direct and indirect couplings and the direction (driver–response relationship) of the considered interaction between different biological time series. We also give their basic theoretical background, their basic requirements for application, their main features and demonstrate their usefulness in different applications in the field of cardiovascular and cardiorespiratory coupling analyses.

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“…Granger [53] was the first study to give the idea about spectral-density approach to test for Granger-causality (GC) which was further elaborated in Geweke [54]. Recently, Breitung and Candelon [55] proposed approach to test GC in the frequency domain taking idea from Granger [53] and Geweke [54].…”

Section: Causality Analysis In the Frequency Domainmentioning

confidence: 99%

“…Recently, Breitung and Candelon [55] proposed approach to test GC in the frequency domain taking idea from Granger [53] and Geweke [54]. The procedure of Breitung and Candelon [56].…”

Section: Causality Analysis In the Frequency Domainmentioning

confidence: 99%

Revisit the Budget Deficits and Inflation: Evidence from Time and Frequency Domain Analyses

Tiwari¹,

Bolat²,

Koçbulut³

2015

TEL

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The purpose of this paper is to test the relationship between budget deficits and inflation for nine EU countries during the period of 1990-2013 using the quarterly data. Recently, the public deficits and inflation have had an increasing importance for developing/emerging and developed countries to build the stability macroeconomic performance in the long run. This study is the first attempt to determine the relationship between the inflation and budget deficits for nine EU countries using different bootstrap causality tests. We employ the bootstrap causality and Granger causality test in the frequency domain analysis which allows us to distinguish short and long-run causality. We do not find a relationship between these variables when we employ bootstrap causality analysis. While the frequency domain causality shows that there is no relationship causality from budget deficits to inflation for all countries, causality from inflation to budget deficits indicates a permanent (long-run) relationship for Belgium, and France.

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Measurement of Linear Dependence and Feedback between Multiple Time Series

Cited by 1,583 publications

References 7 publications

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Cardiovascular and cardiorespiratory coupling analyses: a review

Revisit the Budget Deficits and Inflation: Evidence from Time and Frequency Domain Analyses

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