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## Caracterização da conectividade entre regiões cerebrais via entropia aproximada e causalidade de Granger.; Brain connectivity characterization via approximate entropy and Granger causality.

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 02/08/2011
Português

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56.54%

#Análise de séries temporais#Approximate entropy#Coerência parcial direcionada#Entropia amostral#Entropia aproximada#Inferência estatística#Information theory#Modelos não lineares#Nonlinear models#Partial directed coherence#Sample entropy

Essa dissertação apresenta o desenvolvimento métodos para caracterização da conectividade entre séries temporais neurofisiológicas. Utilizam-se metodologias provenientes da Teoria da Informação Entropias Aproximada e Amostral para representar a complexidade da série no tempo, o que permite inferir como sua variabilidade se transfere a outras sequências, através do uso da coerência parcial direcionada. Para cada sistema analisado: (1) Faz-se uma transformação em outro, relacionando-o às medidas de entropia, (2) Estima-se a conectividade pela coerência parcial direcionada e (3) Avalia-se a robustez do procedimento via simulações de Monte Carlo e análise de sensibilidade. Para os exemplos simulados, a técnica proposta é capaz de oferecer resultados plausíveis, através da correta inferência da direção de conectividade em casos de acoplamento não-linear (quadrático), com número reduzido de amostras temporais dos sinais, em que outras abordagens falham. Embora de simples implementação, conclui-se que o processo mostra-se como uma extensão da causalidade de Granger para o caso não-linear.; The purpose of this work is to present the development of methods for characterizing the connectivity between nonlinear neurophysiological time series. Methodologies from Information Theory Approximate and Sample Entropies are used to represent the complexity of the series in a period of time...

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## Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains

Fonte: Hindawi Publishing Corporation
Publicador: Hindawi Publishing Corporation

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

46.26%

Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ‘‘hidden” Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method.

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## Short run and long run causality in time series: Inference

Fonte: Université de Montréal
Publicador: Université de Montréal

Tipo: Artigo de Revista Científica
Formato: 223846 bytes; application/pdf

Português

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#time series#Granger causality#indirect causality#multiple horizon causality#autoregression#autoregressive model#vector autoregression#VAR#stationary process#nonstationary process#integrated process

We propose methods for testing hypotheses of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy.; Nous proposons des méthodes pour tester des hypothèses de non-causalité à différents horizons, tel que défini dans Dufour et Renault (1998, Econometrica). Nous étudions le cas des modèles VAR en détail et nous proposons des méthodes linéaires basées sur l’estimation d’autorégressions vectorielles à différents horizons. Même si les hypothèses considérées sont non linéaires, les méthodes proposées ne requièrent que des techniques de régression linéaire de même que la théorie distributionnelle asymptotique gaussienne habituelle. Dans le cas des processus intégrés...

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## Nonlinear Causality Testing with Stepwise Multivariate Filtering

Fonte: Instituto Universitário Europeu
Publicador: Instituto Universitário Europeu

Tipo: Trabalho em Andamento
Formato: application/pdf; digital

Português

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56.63%

This study explores the direction and nature of causal linkages among six currencies denoted relative to United States dollar (USD), namely Euro (EUR), Great Britain Pound (GBP), Japanese Yen (JPY), Swiss Frank (CHF), Australian Dollar (AUD) and Canadian Dollar (CAD). These are the most liquid and widely traded currency pairs in the world and make up about 90% of total Forex trading worldwide. The data covers the period 3/20/1987-11/14/2007, including the Asian crisis, the dot-com bubble and the period just before the outbreak of the US subprime crisis. The objective of the paper is to test for the existence of both linear and nonlinear causal relationships among these currency markets. The modified Baek-Brock test for nonlinear non-causality is applied on the currency return time series as well as the linear Granger test. Further to the classical pairwise analysis causality testing is conducted in a multivariate formulation, to correct for the effects of the other variables. A new stepwise multivariate filtering approach is implemented. To check if any of the observed causality is strictly nonlinear, the nonlinear causal relationships of VAR/VECM filtered residuals are also examined. Finally, the hypothesis of nonlinear non-causality is investigated after controlling for conditional heteroskedasticity in the data using GARCH-BEKK...

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## A nonparametric copula based test for conditional independence with applications to granger causality

Fonte: Universidade Carlos III de Madrid
Publicador: Universidade Carlos III de Madrid

Tipo: Trabalho em Andamento
Formato: application/pdf

Publicado em /06/2009
Português

Relevância na Pesquisa

56.53%

#Nonparametric tests#Conditional independence#Granger non-causality#Bernstein density copula#Bootstrap#Finance#Volatility asymmetry#Leverage effect#Volatility feedback effect#Macroeconomics#C12

This paper proposes a new nonparametric test for conditional independence, which is
based on the comparison of Bernstein copula densities using the Hellinger distance.
The test is easy to implement because it does not involve a weighting function in the
test statistic, and it can be applied in general settings since there is no restriction on the
dimension of the data. In fact, to apply the test, only a bandwidth is needed for the
nonparametric copula. We prove that the test statistic is asymptotically pivotal under
the null hypothesis, establish local power properties, and motivate the validity of the
bootstrap technique that we use in finite sample settings. A simulation study illustrates
the good size and power properties of the test. We illustrate the empirical relevance of
our test by focusing on Granger causality using financial time series data to test for
nonlinear leverage versus volatility feedback effects and to test for causality between
stock returns and trading volume. In a third application, we investigate Granger
causality between macroeconomic variables

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## Nonparametric estimation and inference for Granger causality measures

Fonte: Universidade Carlos III de Madrid
Publicador: Universidade Carlos III de Madrid

Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper
Formato: application/pdf

Publicado em 29/03/2012
Português

Relevância na Pesquisa

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#Causality measures#Nonparametric estimation#Time series#Copulas#Bernstein copula density#Local bootstrap#Conditional distribution function#Stock returns#C12#C14#C15

We propose a nonparametric estimator and a nonparametric test for Granger causality measures that quantify linear and nonlinear Granger causality in distribution between random variables. We first show how to write the Granger causality measures in terms of copula densities. We suggest a consistent estimator for these causality measures based on nonparametric estimators of copula densities. Further, we prove that the nonparametric estimators are asymptotically normally distributed and we discuss the validity of a local smoothed bootstrap that we use in finite sample settings to compute a bootstrap bias-corrected estimator and test for our causality measures. A simulation study reveals that the bias-corrected bootstrap estimator of causality measures behaves well and the corresponding test has quite good finite sample size and power properties for a variety of typical data generating processes and different sample sizes. Finally, we illustrate the practical relevance of nonparametric causality measures by quantifying the Granger causality between S&P500 Index returns and many exchange rates (US/Canada, US/UK and US/Japen exchange rates).

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## Carbonomics of the Bangladesh agricultural output: Causality and long-run equilibrium

Fonte: Emerald Group Publishing Ltd
Publicador: Emerald Group Publishing Ltd

Tipo: Artigo de Revista Científica

Publicado em //2013
Português

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#Bangladesh#Agriculture#Developing countries#Econometrics#CO2 emission#Agricultural output#Causality#Long-run equilibrium#Carbonomics

Purpose – The key purpose of this paper is to examine the causality and long-run relationship between CO2 emission and agricultural output for an agriculture-dependent developing country, namely Bangladesh.
Design/methodology/approach – In order to attain the objective, this study has used long-time series data and employed advanced econometric techniques of unit root test, nonlinear least square estimation, Vector Error Correction estimation and Granger causality test.
Findings – The empirical results of the study reveal that Bangladesh agricultural output is not a Granger causal for Bangladesh CO2 emission, but the country's CO2 emission is a Granger causal for its agricultural output. The results also reveal for Bangladesh that any disequilibrium between CO2 emissions and agricultural output could take approximately 17 years to converge to the long-run equilibrium. The results further reveal that the adjustment rate for Bangladesh agricultural output is positive and quite fast at the rate of 69 percent a year. So any disequilibrium will be corrected mostly by the adjustment in Bangladesh agricultural output.
Practical implications – The current CO2 emission in Bangladesh is still below the equilibrium level, which is considered to be an advantage for the country...

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## Statistical inference of nonlinear Granger causality: a semiparametric time series regression analysis.

Fonte: Universidade de Adelaide
Publicador: Universidade de Adelaide

Tipo: Tese de Doutorado

Publicado em //2013
Português

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#time series regression#semiparametric regression#nonlinear Granger causality#partially linear model#estimation and inference

Since the seminal work of Granger (1969), Granger causality has become a useful concept and tool in the study of the dynamic linkages between economic variables and to explore whether or not an economic variable helps forecast another one. Researchers have suggested a variety of methods to test the existence of Grangercausality in the literature. In particular, linear Granger causality testing has been remarkably developed; (see, for example, Toda & Philips (1993), Sims, Stock & Watson (1990), Geweke (1982), Hosoya (1991) and Hidalgo (2000)). However, in practice, the real economic relationship between different variables may often be nonlinear. Hiemstra & Jones (1994) and Nishiyama, Hitomi, Kawasaki & Jeong (2011) recently proposed different methods to test the existence of any non-linear Granger causality between a pair of economic variables under a α-mixing framework of data generating process. Their methods are general with nonparametric features, which however suffer from curse of dimensionality when high lag orders need to be taken into consideration in applications. In this thesis, the main objective is to develop a class of semiparametric time series regression models that are of partially linear structures, with statistical theory established under a more general framework of near epoch dependent (NED) data generating processes...

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## Kernel Granger causality and the analysis of dynamical networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/03/2008
Português

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56.53%

#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Exactly Solvable and Integrable Systems#Quantitative Biology - Quantitative Methods

We propose a method of analysis of dynamical networks based on a recent
measure of Granger causality between time series, based on kernel methods. The
generalization of kernel Granger causality to the multivariate case, here
presented, shares the following features with the bivariate measures: (i) the
nonlinearity of the regression model can be controlled by choosing the kernel
function and (ii) the problem of false-causalities, arising as the complexity
of the model increases, is addressed by a selection strategy of the
eigenvectors of a reduced Gram matrix whose range represents the additional
features due to the second time series. Moreover, there is no {\it a priori}
assumption that the network must be a directed acyclic graph. We apply the
proposed approach to a network of chaotic maps and to a simulated genetic
regulatory network: it is shown that the underlying topology of the network can
be reconstructed from time series of node's dynamics, provided that a
sufficient number of samples is available. Considering a linear dynamical
network, built by preferential attachment scheme, we show that for limited data
use of bivariate Granger causality is a better choice w.r.t methods using $L1$
minimization. Finally we consider real expression data from HeLa cells...

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## Measures of Causality in Complex Datasets with application to financial data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

36.51%

This article investigates the causality structure of financial time series.
We concentrate on three main approaches to measuring causality: linear Granger
causality, kernel generalisations of Granger causality (based on ridge
regression and the Hilbert--Schmidt norm of the cross-covariance operator) and
transfer entropy, examining each method and comparing their theoretical
properties, with special attention given to the ability to capture nonlinear
causality. We also present the theoretical benefits of applying non-symmetrical
measures rather than symmetrical measures of dependence. We apply the measures
to a range of simulated and real data. The simulated data sets were generated
with linear and several types of nonlinear dependence, using bivariate, as well
as multivariate settings. An application to real-world financial data
highlights the practical difficulties, as well as the potential of the methods.
We use two real data sets: (1) U.S. inflation and one-month Libor; (2) S$\&$P
data and exchange rates for the following currencies: AUDJPY, CADJPY, NZDJPY,
AUDCHF, CADCHF, NZDCHF. Overall, we reach the conclusion that no single method
can be recognised as the best in all circumstances, and each of the methods has
its domain of best applicability. We also highlight areas for improvement and
future research.; Comment: 40 pages; 13 figures

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## Extending Granger causality to nonlinear systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/05/2004
Português

Relevância na Pesquisa

46.46%

#Physics - Data Analysis, Statistics and Probability#Physics - Medical Physics#Quantitative Biology - Quantitative Methods

We consider extension of Granger causality to nonlinear bivariate time
series. In this frame, if the prediction error of the first time series is
reduced by including measurements from the second time series, then the second
time series is said to have a causal influence on the first one. Not all the
nonlinear prediction schemes are suitable to evaluate causality, indeed not all
of them allow to quantify how much the knowledge of the other time series
counts to improve prediction error. We present a novel approach with bivariate
time series modelled by a generalization of radial basis functions and show its
application to a pair of unidirectionally coupled chaotic maps and to a
physiological example.; Comment: 8 pages, 4 figures

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## Granger causality and the inverse Ising problem

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

56.41%

#Quantitative Biology - Neurons and Cognition#Condensed Matter - Disordered Systems and Neural Networks#Physics - Data Analysis, Statistics and Probability

We study Ising models for describing data and show that autoregressive
methods may be used to learn their connections, also in the case of asymmetric
connections and for multi-spin interactions. For each link the linear Granger
causality is two times the corresponding transfer entropy (i.e. the information
flow on that link) in the weak coupling limit. For sparse connections and a low
number of samples, the L1 regularized least squares method is used to detect
the interacting pairs of spins. Nonlinear Granger causality is related to
multispin interactions.; Comment: 6 pages and 8 figures. Revised version in press on Physica A

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## Granger causality for circular variables

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/02/2009
Português

Relevância na Pesquisa

56.41%

#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Physics - Data Analysis, Statistics and Probability#Quantitative Biology - Neurons and Cognition

In this letter we discuss use of Granger causality to the analyze systems of
coupled circular variables, by modifying a recently proposed method for
multivariate analysis of causality. We show the application of the proposed
approach on several Kuramoto systems, in particular one living on networks
built by preferential attachment and a model for the transition from deeply to
lightly anaesthetized states. Granger causalities describe the flow of
information among variables.; Comment: 4 pages, 5 figures

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## Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

46.39%

We propose a general matrix-valued multiple kernel learning framework for
high-dimensional nonlinear multivariate regression problems. This framework
allows a broad class of mixed norm regularizers, including those that induce
sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel
Hilbert Spaces. We develop a highly scalable and eigendecomposition-free
algorithm that orchestrates two inexact solvers for simultaneously learning
both the input and output components of separable matrix-valued kernels. As a
key application enabled by our framework, we show how high-dimensional causal
inference tasks can be naturally cast as sparse function estimation problems,
leading to novel nonlinear extensions of a class of Graphical Granger Causality
techniques. Our algorithmic developments and extensive empirical studies are
complemented by theoretical analyses in terms of Rademacher generalization
bounds.; Comment: 22 pages. Presentation changes; Corrections made to Theorem 2
(section 6.2) in this version

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## Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/08/2014
Português

Relevância na Pesquisa

46.39%

We propose a general matrix-valued multiple kernel learning framework for
high-dimensional nonlinear multivariate regression problems. This framework
allows a broad class of mixed norm regularizers, including those that induce
sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel
Hilbert Spaces. We develop a highly scalable and eigendecomposition-free
algorithm that orchestrates two inexact solvers for simultaneously learning
both the input and output components of separable matrix-valued kernels. As a
key application enabled by our framework, we show how high-dimensional causal
inference tasks can be naturally cast as sparse function estimation problems,
leading to novel nonlinear extensions of a class of Graphical Granger Causality
techniques. Our algorithmic developments and extensive empirical studies are
complemented by theoretical analyses in terms of Rademacher generalization
bounds.; Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty
in Artificial Intelligence (UAI2013)

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## Analyzing Multiple Nonlinear Time Series with Extended Granger Causality

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/05/2004
Português

Relevância na Pesquisa

56.74%

#Nonlinear Sciences - Chaotic Dynamics#Mathematics - Statistics Theory#Physics - Data Analysis, Statistics and Probability

Identifying causal relations among simultaneously acquired signals is an
important problem in multivariate time series analysis. For linear stochastic
systems Granger proposed a simple procedure called the Granger causality to
detect such relations. In this work we consider nonlinear extensions of
Granger's idea and refer to the result as Extended Granger Causality. A simple
approach implementing the Extended Granger Causality is presented and applied
to multiple chaotic time series and other types of nonlinear signals. In
addition, for situations with three or more time series we propose a
conditional Extended Granger Causality measure that enables us to determine
whether the causal relation between two signals is direct or mediated by
another process.; Comment: 16 pages, 6 figures

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## Kernel method for nonlinear Granger causality

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

66.59%

#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Exactly Solvable and Integrable Systems

Important information on the structure of complex systems, consisting of more
than one component, can be obtained by measuring to which extent the individual
components exchange information among each other. Such knowledge is needed to
reach a deeper comprehension of phenomena ranging from turbulent fluids to
neural networks, as well as complex physiological signals. The linear Granger
approach, to detect cause-effect relationships between time series, has emerged
in recent years as a leading statistical technique to accomplish this task.
Here we generalize Granger causality to the nonlinear case using the theory of
reproducing kernel Hilbert spaces. Our method performs linear Granger causality
in the feature space of suitable kernel functions, assuming arbitrary degree of
nonlinearity. We develop a new strategy to cope with the problem of
overfitting, based on the geometry of reproducing kernel Hilbert spaces.
Applications to coupled chaotic maps and physiological data sets are presented.; Comment: Revised version, accepted for publication on Physical Review Letters

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## Granger Causality and Cross Recurrence Plots in Rheochaos

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/11/2007
Português

Relevância na Pesquisa

66.39%

Our stress relaxation measurements on wormlike micelles using a Rheo-SALS
(rheology + small angle light scattering) apparatus allow simultaneous
measurements of the stress and the scattered depolarised intensity. The latter
is sensitive to orientational ordering of the micelles. To determine the
presence of causal influences between the stress and the depolarised intensity
time series, we have used the technique of linear and nonlinear Granger
causality. We find there exists a feedback mechanism between the two time
series and that the orientational order has a stronger causal effect on the
stress than vice versa. We have also studied the phase space dynamics of the
stress and the depolarised intensity time series using the recently developed
technique of cross recurrence plots (CRPs). The presence of diagonal line
structures in the CRPs unambiguously proves that the two time series share
similar phase space dynamics.; Comment: 10 pages, 7 figures

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## Granger Causality in Multi-variate Time Series using a Time Ordered Restricted Vector Autoregressive Model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/11/2015
Português

Relevância na Pesquisa

46.58%

#Statistics - Methodology#Mathematics - Statistics Theory#Physics - Data Analysis, Statistics and Probability#Statistics - Computation#Statistics - Machine Learning

Granger causality has been used for the investigation of the inter-dependence
structure of the underlying systems of multi-variate time series. In
particular, the direct causal effects are commonly estimated by the conditional
Granger causality index (CGCI). In the presence of many observed variables and
relatively short time series, CGCI may fail because it is based on vector
autoregressive models (VAR) involving a large number of coefficients to be
estimated. In this work, the VAR is restricted by a scheme that modifies the
recently developed method of backward-in-time selection (BTS) of the lagged
variables and the CGCI is combined with BTS. Further, the proposed approach is
compared favorably to other restricted VAR representations, such as the
top-down strategy, the bottom-up strategy, and the least absolute shrinkage and
selection operator (LASSO), in terms of sensitivity and specificity of CGCI.
This is shown by using simulations of linear and nonlinear, low and
high-dimensional systems and different time series lengths. For nonlinear
systems, CGCI from the restricted VAR representations are compared with
analogous nonlinear causality indices. Further, CGCI in conjunction with BTS
and other restricted VAR representations is applied to multi-channel scalp
electroencephalogram (EEG) recordings of epileptic patients containing
epileptiform discharges. CGCI on the restricted VAR...

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## Nonlinear parametric model for Granger causality of time series

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/02/2006
Português

Relevância na Pesquisa

56.46%

#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics#Computer Science - Learning#Physics - Medical Physics#Quantitative Biology - Quantitative Methods

We generalize a previously proposed approach for nonlinear Granger causality
of time series, based on radial basis function. The proposed model is not
constrained to be additive in variables from the two time series and can
approximate any function of these variables, still being suitable to evaluate
causality. Usefulness of this measure of causality is shown in a physiological
example and in the study of the feed-back loop in a model of excitatory and
inhibitory neurons.; Comment: 4 pages 5 figures

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