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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.

Massaroppe, Lucas
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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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...

Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains

Krumin, Michael; Shoham, Shy
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.

Short run and long run causality in time series: Inference

DUFOUR, Jean-Marie; PELLETIER, Denis; RENAULT, Éric
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 223846 bytes; application/pdf
Português
Relevância na Pesquisa
46.25%
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...

Nonlinear Causality Testing with Stepwise Multivariate Filtering

BEKIROS, Stelios D.
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...

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

Bouezmarni, Taoufik; Rombouts, Jeroen V. K.; Taamouti, Abderrahim
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /06/2009 Português
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56.53%
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

Nonparametric estimation and inference for Granger causality measures

Taamouti, Abderrahim; Bouezmarni, Taoufik; El Ghouch, Anouar
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
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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).

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

Murad, Wahid; Ratnatunga, Janek
Fonte: Emerald Group Publishing Ltd Publicador: Emerald Group Publishing Ltd
Tipo: Artigo de Revista Científica
Publicado em //2013 Português
Relevância na Pesquisa
46.45%
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...

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

Lee, Sooyoung
Fonte: Universidade de Adelaide Publicador: Universidade de Adelaide
Tipo: Tese de Doutorado
Publicado em //2013 Português
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97.03%
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...

Kernel Granger causality and the analysis of dynamical networks

Marinazzo, Daniele; Pellicoro, Mario; Stramaglia, Sebastiano
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/03/2008 Português
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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...

Measures of Causality in Complex Datasets with application to financial data

Zaremba, Anna; Aste, Tomaso
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

Extending Granger causality to nonlinear systems

Ancona, Nicola; Marinazzo, Daniele; Stramaglia, Sebastiano
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/05/2004 Português
Relevância na Pesquisa
46.46%
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

Granger causality and the inverse Ising problem

Pellicoro, Mario; Stramaglia, Sebastiano
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
56.41%
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

Granger causality for circular variables

Angelini, Leonardo; Pellicoro, Mario; Stramaglia, Sebastiano
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/02/2009 Português
Relevância na Pesquisa
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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

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

Sindhwani, Vikas; Quang, Minh Ha; Lozano, Aurelie C.
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

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

Sindhwani, Vikas; Minh, Ha Quang; Lozano, Aurelie
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)

Analyzing Multiple Nonlinear Time Series with Extended Granger Causality

Chen, Yonghong; Rangarajan, Govindan; Feng, Jianfeng; Ding, Mingzhou
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/05/2004 Português
Relevância na Pesquisa
56.74%
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

Kernel method for nonlinear Granger causality

Marinazzo, Daniele; Pellicoro, Mario; Stramaglia, Sebastiano
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
66.59%
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

Granger Causality and Cross Recurrence Plots in Rheochaos

Ganapathy, Rajesh; Rangarajan, Govindan; Sood, A. K.
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

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

Siggiridou, Elsa; Kugiumtzis, Dimitris
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/11/2015 Português
Relevância na Pesquisa
46.58%
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...

Nonlinear parametric model for Granger causality of time series

Marinazzo, Daniele; Pellicoro, Mario; Stramaglia, Sebastiano
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/02/2006 Português
Relevância na Pesquisa
56.46%
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