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

Multiscale Granger causality

In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the dynamic complexity of individual processes at different time scales are well-established, multiscale analysis of directed interactions has never been formalized theoretically, and empirical evaluations are complicated by practical issues such as filtering and downsampling. Here we extend the very popular measure of Granger causality (GC), a prominent tool for assessing directed lagged interactions between joint processes, to quantify information transfer across multiple time scales. We show that the multiscale processing of a vector autoregressive (AR) process introduces a moving average (MA) component, and describe how to represent the resulting ARMA process using state space (SS) models and to combine the SS model parameters for computing exact GC values at arbitrarily large time scales. We exploit the theoretical formulation to identify peculiar features of multiscale GC in basic AR processes, and demonstrate with numerical simulations the much larger estimation accuracy of the SS approach compared with pure AR modeling of filtered and downsampled data. The improved computational reliability is exploited to disclose meaningful multiscale patterns of information transfer between global temperature and carbon dioxide concentration time series, both in paleoclimate and in recent years

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.

Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data

It is often useful in multivariate time series analysis to determine statistical causal relations between different time series. Granger causality is a fundamental measure for this purpose. Yet the traditional pairwise approach to Granger causality analysis may not clearly distinguish between direct causal influences from one time series to another and indirect ones acting through a third time series. In order to differentiate direct from indirect Granger causality, a conditional Granger causality measure in the frequency domain is derived based on a partition matrix technique. Simulations and an application to neural field potential time series are demonstrated to validate the method.Comment: 18 pages, 6 figures, Journal publishe

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

On the dynamics of energy consumption and employment in public and private sector.

This study intended to analyze the direction of Granger-causality between energy consumption and employment in public and private sector. We have adopted DL approach for Granger-causality analysis. We found from the whole analysis that there is evidence of bidirectional causality between energy consumption and employment in organized public and private sector. Therefore our study supports for our third testable hypothesis i.e., “feedback hypothesis”.Energy consumption, Public and Private sector employment, Granger causality.

Tourism, real output and real effective exchange rate in Malaysia: a view from rolling sub-samples

The objective of this study is to examine the tourism-growth nexus for Malaysia with the cointegration and Granger causality tests. This study covers the monthly data from January 1989 to May 2010. The Johansen’s cointegration and the residuals-based test for cointegration with regime shift consistently suggest that tourist arrivals, real output, and real effective exchange rate in Malaysia are cointegrated. In terms of Granger causality, this study finds different sources of causality. In the short run, real output and real effective exchange rate Granger-cause tourist arrivals, while tourists arrivals also Granger-cause real output and real effective exchange rate. In the long run, this study shows that all the variables are bi-directional causality. Moreover, we also extend the study to analyse the stability of causality between tourism and real output by using rolling regression procedure into the Granger causality test. Interestingly, the rolling Granger causality test demonstrates that the growth-led tourism hypothesis is valid and stable, while tourism-led growth hypothesis is valid and but unstable in particular after 2005. Although tourism contributes to economic growth, it is not a persistence source for long-term economic growth in Malaysia.tourism-led growth hypothesis; Malaysia; rolling regression

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