Analyzing Multiple Nonlinear Time Series with Extended Granger Causality

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 figure

An Out of Sample Test for Granger Causality

Granger (1980) summarizes his personal viewpoint on testing for causality, and outlines what he considers to be a useful operational version of his original definition of causality (Granger (1969)), which he notes was partially alluded to in Wiener (1958). This operational version is based on a comparison of the 1-step ahead predictive ability of competing models. However, Granger concludes his discussion by noting that it is common practice to test for Granger causality using in-sample F-tests. The practice of using in-sample type Granger causality tests continues to be prevalent. In this paper we develop simple (nonlinear) out-of-sample predictive ability tests of the Granger non-causality null hypothesis. In addition, Monte Carlo experiments are used to investigate the finite sample properites of the test. An empirical illustration shows that the choice of in-sample versus out-of-sample Granger causality tests can crucially affect the conclusions about the predictive content of money for output.

Decomposing Granger causality over the spectrum.

We develop a bivariate spectral Granger-causality test that can be applied at each individual frequency of the spectrum. The spectral approach to Granger causality has the distinct advantage that it allows to disentangle (potentially) different Granger-causality relationships over different time horizons. We illustrate the usefulness of the proposed approach in the context of the predictive value of European production expectation surveys.Business surveys; Frequency; Granger causality; Production expectations; Spectral analysis; Surveys; Time; Value;

Multivariate Granger Causality and Generalized Variance

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables, but may occur among groups, or "ensembles", of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer new justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy". Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28 pages, 3 figures, 1 table, LaTe

The Granger-Causality between Transportation and GDP: A Panel Data Approach

This study investigates the Granger-causality relationship between real per capita GDP and transportation of EU-15 countries using a panel data set covering the period 1970-2008. Our findings indicate that the dominant type of Granger-causality is bidirectional. Accordingly, we conclude that care must be paid in defining the dependent and independent variables when studying the relationship between transportation and income. Instances of one-way or no Granger-causality were found to correspond with countries with the lowest income per capita ranks in 1970 and/or in 2008, including Portugal, Greece and Italy. We speculate that bi-directional Granger causality between income and transportation is observed only after an economy has completed its transition in terms of economic development.Granger-causality, Transportation, Income

Looking behind Granger causality

Granger causality as a popular concept in time series analysis is widely applied in empirical research. The interpretation of Granger causality tests in a cause-effect context is, however, often unclear or even controversial, so that the causality label has faded away. Textbooks carefully warn that Granger causality does not imply true causality and preferably refer the Granger causality test to a forecasting technique. Applying theory of inferred causation, we develop in this paper a method to uncover causal structures behind Granger causality. In this way we re-substantialize the causal attribution in Granger causality through providing an causal explanation to the conditional dependence manifested in Granger causality.Granger Causality; Time Series Causal Model; Graphical Model

Trade and GDP Growth in Morocco: Short-run or Long-run Causality?

This study utilizes cointegration and Granger-causality tests to examine the relationship between trade and economic growth in Morocco over the period 1960-2000 using the VEC model. The result indicate that both exports and imports enter with positive signs in the cointegration equation. The results show that imports and exports Granger caused GDP and imports Granger caused exports. These results can be interpreted as a causality from the foreign sector to the domestic growth of Morocco. Import expansion increases exports that affect the GDP growth.GDP, Exports, Imports, Granger Causality, Cointegration

The Granger Non-Causality Test in Cointegrated Vector Autoregressions

In general, Wald tests for the Granger non-causality in vector autoregressive (VAR) process are known to have non-standard asymptotic properties for cointegrated systems. However, that may have standard asymptotic properties depending on the rank of the submatrix of cointegration. In this paper, we propose a procedure for conducting Granger non-causality tests that are based on discrimination of these asymptotic properties. This paper also investigate the finite sample performance of our testing procedure, and compare the testing procedure with conventional causality tests in levels VARfs.Vector autoregression, Cointegration, Granger causality, Hypothesis testing

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. In this paper we propose multivariate out-of-sample tests for Granger causality. The performance of the out-of-sample tests is measured by a simulation study and 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, we investigate whether the consumer confidence index Granger causes retail sales in Germany, France, the Netherlands and Belgium.Consumer Sentiment, Granger Causality, Multivariate Time Series,Out-of-sample TestsBelgium; Consumer confidence; Consumer Confidence Index; Consumer sentiment; Data; Forecasting; Germany; Granger causality; Indexes; Multivariate time series; Out-of-sample tests; Performance; Power; Regression; Research; Sales; Simulation; Studies; Tests; Time; Time series;

Temporal Aggregation, Causality Distortions, and a Sign Rule

Temporally aggregated data is a bane for Granger causality tests. The same set of variables may lead to contradictory causality inferences at different levels of temporal aggregation. Obtaining temporally disaggregated data series is impractical in many situations. Since cointegration is invariant to temporal aggregation and implies Granger causality this paper proposes a sign rule to establish the direction of causality. Temporal aggregation leads to a distortion of the sign of the adjustment coefficients of an error correction model. The sign rule works better with highly temporally aggregated data. The practitioners, therefore, may revert to using annual data for Granger causality testing instead of looking for quarterly, monthly or weekly data. The method is illustrated through three applications.Granger causality test, cointegration, error correction model, adjustment coefficient, sign rule