Linear Granger Causality Research Articles

Testing conditional independence via empirical likelihood

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an asymptotic optimality property in terms of average power. Simulations suggest that the tests are well behaved in finite samples. Applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear Granger causality test fails to detect.

Measures of Causality in Complex Datasets with Application to Financial Data

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.

Linear and non-linear causality between price indices and commodity prices

We apply linear and non-linear Granger causality tests to four U.S. price indices and 31 commodity series, which expand a 54-year period (January 1957–December 2011). We find evidence of linear Granger causality mostly from individual commodities to price indices. The latter, however, seem to Granger-cause individual commodity prices in a non-linear fashion. Overall, our estimation results show that Agricultural raw materials (cotton, hides, rubber, and wool), Beverages (coffee), Food (maize, rice, and wheat), Minerals, ores and metals (copper), and Vegetable oilseeds and oils (groundnut oil and soybean oil) display bidirectional linear and non-linear feedback effects vis-à-vis price indices. These findings suggest that not only shocks on commodity demand and supply may impact aggregate price indices, but also that non-commodity shocks, embodied in aggregate price indices, may impact commodity prices linearly and nonlinearly.

Pair-wise Clustering of Large Scale Granger Causality Index Matrices for Revealing Communities.

The analysis of large ensembles of time series is a fundamental challenge in different domains of biomedical image processing applications, specifically in the area of functional MRI data processing. An important aspect of such analysis is the ability to reconstruct community network structures based on interactive behavior between different nodes of the network which are captured in such time series. In this study, we start with a previously proposed novel approach that applies the linear Granger Causality concept to very high-dimensional time series. This approach is based on integrating dimensionality reduction into a multivariate time series model. If residuals of dimensionality reduced models can be transformed back into the original space, prediction errors in the high-dimensional space may be computed, and a large scale Granger Causality Index (lsGCI) is properly defined. The primary goal of this study was then to present an approach for recovering network structure from such lsGCI interactions through the application of pair-wise clustering. We specifically focus on a clustering approach based on topographic mapping of proximity data (TMP) for this purpose. We demonstrate our approach with a simulated network composed of five pair-wise different internal networks with varying strengths of community structure (based on the number of inter-network vertices). Our results suggest that such pair-wise clustering with TMP is capable of reconstructing the structure of the original network from lsGCI matrices that record the interactions between different nodes of the network when there is sufficient disparity between the intra- and inter-network vertices.

Application of adaptive nonlinear Granger causality: Disclosing network changes before and after absence seizure onset in a genetic rat model

Advanced methods of signal analysis of the preictal and ictal activity dynamics characterizing absence epilepsy in humans with absences and in genetic animal models have revealed new and unknown electroencephalographic characteristics, that has led to new insights and theories. Taking into account that some network associations can be considered as nonlinear, an adaptive nonlinear Granger causality approach was developed and applied to analyze cortico-cortical, cortico-thalamic and intrathalamic network interactions from local field potentials (LFPs). The outcomes of adaptive nonlinear models, constructed based on the properties of electroencephalographic signal and on statistical criteria to optimize the number of coefficients in the models, were compared with the outcomes of linear Granger causality. The nonlinear adaptive method showed statistically significant preictal changes in Granger causality in almost all pairs of channels, as well as ictal changes in cortico-cortical, cortico-thalamic and intrathalamic networks. Current results suggest rearrangement of interactions in the thalamo-cortical network accompanied the transition from preictal to ictal phase. The linear method revealed no preictal and less ictal changes in causality. Achieved results suggest that this proposed adaptive nonlinear method is more sensitive than the linear one to dynamics of network properties. Since changes in coupling were found before the seizure-related increase of LFP signal amplitude and also based on some additional tests it seems likely that they were not spurious and could not result from signal to noise ratio change.

Does fine wine price contain useful information to forecast GDP? Evidence from major developed countries

This study provides the first attempt to examine the ability of the price of fine wine to forecast the Gross Domestic Product (GDP) for the major developed countries. Considering the limitation of a linear Granger causality test in detecting nonlinear causal relationships, a nonlinear Granger causality test is also employed. The results from our nonlinear causality test show that this new variable contains useful information to forecast GDP for the US, the UK, and Australia, suggesting that we may include it as a forecasting variable in GDP forecasting models, especially nonlinear models, for these three countries.

How strong are the causal relationships between Islamic stock markets and conventional financial systems? Evidence from linear and nonlinear tests

Past studies suggest that the Islamic finance system is only weakly linked or even decoupled from conventional markets. If this statement is true, then this system may provide a cushion against potential losses resulting from probable future financial crises. In this article, we make use of heteroscedasticity-robust linear Granger causality and nonlinear Granger causality tests to examine the links between the Islamic and global conventional stock markets, and between the Islamic stock market and several global economic and financial shocks. Our findings reveal evidence of significant linear and nonlinear causality between the Islamic and conventional stock markets but more strongly from the Islamic stock market to the other markets. They also show potent causality between the Islamic stock market and financial and risk factors. This evidence leads to the rejection of the hypothesis of decoupling of the Islamic market from their conventional counterparts, thereby reduces the portfolio benefits from diversification with Sharia-based markets. A striking result shows a connection between the Islamic stock market and interest rates and interest-bearing securities, which is inconsistent with the Sharia rules. The results also suggest that modeling Islamic stock markets should be done within a nonlinear VAR system and not through a regression equation.

Electricity Consumption and Economic Growth in Turkey: Cointegration, Linear and Nonlinear Granger Causality

The purpose of this study is to examine causal relationships between the electricity consumption and economic growth in Turkey for the period 1967–2007. To accomplish this purpose, we utilize three analytical tools in time series econometrics: The bounds testing cointegration approach, the linear Granger causality test and the nonlinear Granger causality test. We depart from the existing literature on the energy consumption and economic growth nexus in Turkey by testing nonlinearity in the series and carrying out the nonlinear Granger causality test. The cointegration analysis shows that the electricity consumption and economic growth are cointegrated in the long-run. The linear Granger causality test based on the error correction model shows the bi-directional Granger causality in both the short- and the long-run between the electricity consumption and economic growth in Turkey. After filtering out the linear properties of the series with cointegration analysis, we carry out the Brock, Dechert, and Scheinkman nonlinearity test and find evidence of nonlinearity in the series. Therefore, the inferences from the nonlinear Granger causality test are more appropriate than the linear Granger causality analysis for Turkey. The nonlinear causality analysis supports the neutrality hypothesis, implying that electricity conservation policy will not damage the growth in the Turkish economy.

Causal and Structural Connectivity of Pulse-Coupled Nonlinear Networks

We study the reconstruction of structural connectivity for a general class of pulse-coupled nonlinear networks and show that the reconstruction can be successfully achieved through linear Granger causality (GC) analysis. Using spike-triggered correlation of whitened signals, we obtain a quadratic relationship between GC and the network couplings, thus establishing a direct link between the causal connectivity and the structural connectivity within these networks. Our work may provide insight into the applicability of GC in the study of the function of general nonlinear networks.

Coherence analysis overestimates the role of baroreflex in governing the interactions between heart period and systolic arterial pressure variabilities during general anesthesia

During general anesthesia positive pressure mechanical ventilation (MV) profoundly affects intrathoracic pressure and venous return, thus soliciting cardiopulmonary reflexes and modifying stroke volume. As a consequence heart period, approximated as the temporal distance between two consecutive R peaks on the ECG (RR), and systolic arterial pressure (SAP) variability series are usually highly correlated at the MV frequency (MVF) and this significant correlation is commonly taken as an indication of an active baroreflex. In this study the involvement of baroreflex was tested according to a time-domain linear Granger causality approach accounting explicitly for MV in two experimental protocols. In the first protocol volatile (VA) or intravenous (IA) anesthetic was administered in humans during pressure controlled MV (PCMV). In the second protocol IA was administered in pigs during PCMV or pressure support MV (PSMV). Causality analysis was contrasted with RR-SAP squared coherence. Significant coherence values at MVF were always found in both protocols. On the contrary, a significant causal link from SAP to RR was less frequently found in humans independently of the anesthesiological strategy and in animals during PCMV. PSMV was superior to PCMV in animals because it was able to better preserve a link from SAP to RR. During general anesthesia the involvement of baroreflex in governing RR-SAP variability interactions is largely overestimated by RR-SAP squared coherence and causality analysis can be exploited to rank anesthesiological strategies and MV modes according to the ability of preserving a working baroreflex.

Exploring Effective Connectivity by a Granger Causality Approach with Embedded Dimension Reduction

We propose applying the linear Granger Causality concept to very high-dimensional time series. The approach is based on integrating dimensionality reduction into a multivariate time series model. If residuals of dimensionality reduced models can be transformed back into the original space, prediction errors in the high–dimensional space may be computed, and a Granger Causality Index (GCI) is properly defined. We provide a proof–of–principle, and compare the results with the classical GCI.

Long- and Short-Run Relationships between House and Stock Prices in South Africa: A Nonparametric Approach

This paper provides empirical evidence on the long- and short-run relationships between real house and stock prices of South Africa. Standard linear tests may not detect the existence of these relationships between time series especially in the presence of structural shifts or regime changes, which, in turn, may cause nonlinearities in the observed series. Thus, in this study, both linear and nonparametric cointegration and Granger causality tests were conducted. Results from the linear cointegration test showed no long-run relationship between house and stock prices. The linear Granger causality test produced no evidence of causality either. In contrast, the nonparametric cointegration test revealed a long-run one-to-one relationship between the two series, with the nonparametric Granger causality test indicating a bi-directional causality. Therefore, stability in the housing market drives stability in the equity market and vice versa.

The equivalence of linear Gaussian connectivity techniques

The theoretical basis of linear Gaussian connectivity methods for the analysis of fMRI data is examined in this article, resulting in a clarification of methodological dependencies between techniques. In particular, Granger causality connectivity procedures, which describe instantaneous and directed influence between sets of voxel timeseries, are shown to be remappings of correlation-based metrics. Furthermore, the statistical inference tests applied to pairwise Granger causality measures are theoretically shown to be equivalent to inference tests applied to correlation-based metrics. These results are demonstrated empirically using receiver operating characteristic curves derived from vector autoregressive models of various lags, sample size, and noise covariance values. The equivalence of linear Granger causality and correlation-based methods, in both metric and test statistic, renders linear Granger causality a restatement of traditional data-driven methodologies in the context of brain connectivity studies. Furthermore, the equivalence highlights the centrality of partial correlation and partial variance in linear connectivity analyses and bridges the gap between functional and effective connectivity techniques. Consequently, rather than a distinction rooted in methodological difference, the dichotomy between functional and effective connectivity methods is ultimately a function of model configuration realized in choices such as the selection of nodes, the choice to model instantaneous and/or directed influence, and the choice to employ many bivariate models or a single multivariate model. While these theoretical results may be unsurprising to the reader with advanced statistical knowledge, they highlight the importance of a clear understanding of the theoretical basis of connectivity analysis methods for human brain mapping researchers.

Adaptive estimation of vector autoregressive models with time-varying variance: Application to testing linear causality in mean

Linear vector autoregressive (VAR) models where the innovations could be unconditionally heteroscedastic are considered. The volatility structure is deterministic and quite general, including breaks or trending variances as special cases. In this framework we propose ordinary least squares (OLS), generalized least squares (GLS) and adaptive least squares (ALS) procedures. The GLS estimator requires the knowledge of the time-varying variance structure while in the ALS approach the unknown variance is estimated by kernel smoothing with the outer product of the OLS residual vectors. Different bandwidths for the different cells of the time-varying variance matrix are also allowed. We derive the asymptotic distribution of the proposed estimators for the VAR model coefficients and compare their properties. In particular we show that the ALS estimator is asymptotically equivalent to the infeasible GLS estimator. This asymptotic equivalence is obtained uniformly with respect to the bandwidth(s) in a given range and hence justifies data-driven bandwidth rules. Using these results we build Wald tests for the linear Granger causality in mean which are adapted to VAR processes driven by errors with a nonstationary volatility. It is also shown that the commonly used standard Wald test for the linear Granger causality in mean is potentially unreliable in our framework (incorrect level and lower asymptotic power). Monte Carlo experiments illustrate the use of the different estimation approaches for the analysis of VAR models with time-varying variance innovations.

Examining Granger causality between atmospheric parameters and radon

In this paper, we study the relationship between atmospheric parameters (i.e., temperature and humidity) and radon data. We use the linear Granger causality in order to observe possible connections, on short and mid time scale periods, between radon time series and meteorological parameters that strongly influence radon emissions. The analysis suggests radon emission is not affected by these atmospheric parameters on short periods, while there is an evidence of Granger causality on mid periods.

Assessing Granger non-causality using nonparametric measure of conditional independence.

In recent years, Granger causality has become a popular method in a variety of research areas including engineering, neuroscience, and economics. However, despite its simplicity and wide applicability, the linear Granger causality is an insufficient tool for analyzing exotic stochastic processes such as processes involving non-linear dynamics or processes involving causality in higher order statistics. In order to analyze such processes more reliably, a different approach toward Granger causality has become increasingly popular. This new approach employs conditional independence as a tool to discover Granger non-causality without any assumption on the underlying stochastic process. This paper discusses the concept of discovering Granger non-causality using measures of conditional independence, and proposes a novel measure of conditional independence. In brief, the proposed approach estimates the conditional distribution function through a kernel based least square regression approach. This paper also explores the strengths and weaknesses of the proposed method compared to other available methods, and provides a detailed comparison of these methods using a variety of synthetic data sets.

Cointegration, Linear and Nonlinear Causality among Futures with Different Maturities: Evidence from Indian Agricultural Commodity Futures Markets

The paper aims to study the market efficiency, unbiasedness and direction of causality among four agricultural commodities futures contracts traded at National Commodity & Derivatives Exchange Ltd. (NCDEX). The study has tested the efficiency and unbiasedness using Johansen's Cointegration approach and direction of causality using linear Toda and Yamamoto (1995) and the nonparametric Diks and Panchenko (2006) causality for forecasting horizons of 28 days, 56 days and 84 days. The study also takes into account the possible effects of cointegration on both linear and nonlinear Granger causality tests. The results of unfiltered linear granger causality provide support to a stronger flow of information from spot to futures. However when cointegration is modeled the causality disappears. The results have important implications on the previous research done on the same issue. Ignoring cointegration among spot and futures prices may result in improperly concluding linear/nonlinear causality in either direction. Further inability of futures to lead spot market urge for further reforms in the agricultural commodity futures through increasing awareness, wider participation, better infrastructure etc. so as to make futures market more efficient in the long run and perform their role of price discovery and risk management more efficiently and effectively.

A contribution to attribution of recent global warming by out‐of‐sample Granger causality analysis

AbstractThe topic of attribution of recent global warming is usually faced by studies performed through global climate models (GCMs). Even simpler econometric models have been applied to this problem, but they led to contrasting results. In this article, we show that a genuine predictive approach of Granger analysis leads to overcome problems shown by these models and to obtain a clear signal of linear Granger causality from greenhouse gases (GHGs) to the global temperature of the second half of the 20th century. In contrast, Granger causality is not evident using time series of natural forcing. Copyright © 2011 Royal Meteorological Society

Testing instantaneous linear Granger causality in presence of nonlinear dynamics

This Note is devoted to the test of instantaneous linear Granger causality when the errors are dependent but uncorrelated. The assumptions are weak and include a large set of dynamics as for instance the GARCH processes. We show that the standard Wald test for testing instantaneous linear Granger causality is not valid in our framework. As a consequence Wald tests which are valid in our framework are proposed.

Granger causal relations among Greater China stock markets: a nonlinear perspective

This article uses linear and nonlinear Granger causality tests to study Granger causal relations among the stock markets of Greater China. In sharp contrast to the results disclosed by its linear counterpart, a nonlinear causality test provides evidence of isolated bi-directional causal relations between two Chinese stock markets and between the HKSE and the TWSE in the earlier period of 1992 to 1999. The nonlinear causality test further shows that, in the later period of 2000 to 2008, Granger causal relations have been strengthened and that Chinese stock markets are well connected with their neighbour markets, the HKSE and the TWSE, and they are playing a most influential role among the stock markets of Greater China.