Time Domain Granger Causality Research Articles

The nexus between remittance, exchange rate and economic growth of E7 economies: Frequency domain analysis

This study investigates the nexus between economic growth (GDP), trade openness, remittances, exchange rate, and agricultural output in E7 (Russia, Indonesia, Mexico, China, India, Brazil, and Turkey) economies, covering the data from 1990 to 2020. In the first step, we adopted the Dumitrescu and Hurlin time domain Granger causality test, which shows that economic growth (GDP) and agriculture do not have any causal relationship, not even at 3-lags. However, uni-directional causality exists between agriculture and economic growth at the first level difference. In the second step, we used Granger causality analysis in the frequency domain, presented by Croux and Reusens, showing a bivariate correlation among economic growth, trade, remittance, and agricultural output. The panel Granger causality outcome indicated that the causality between variables with various frequencies differs. Policymakers in these economies may consider these pragmatic results to formulate valuable and appropriate short-, medium-, and long-term economic strategies.

Economic Growth, Exchange Rate and Remittance Nexus: Evidence from Africa

This paper examined the nexus between economic growth and exchange rate, remittances, trade, and agricultural output based on data sourced from 1980 to 2018 for 10 selected African economies. We employed both the Dumitrescu and Hurlin time-domain Granger causality test and the Croux and Reusens frequency domain Granger causality test. Results from the time-domain test suggests that causality only exists between economic growth and both exchange rate and trade, with no significant relationship between economic growth and both remittances and agricultural output. When we employed frequency domain model in our analysis, the results suggested that there is a bi-directional temporary and permanent causality between economic growth and exchange rate, trade, agriculture, and remittances. Our results suggest the validity of both the J-Curve and Marshall–Lerner hypotheses in the studied economies. Our study offers some relevant policy implications.

Technical considerations on the use of Granger causality in neuromonitoring

Neuromonitoring-derived indices play an important role in implementing personalised medicine for traumatic brain injury patients. A well-established example is the pressure reactivity index (PRx), calculated from spontaneous fluctuations of arterial blood pressure (ABP) and intracranial pressure (ICP). PRx assumes causal relationship between ABP and ICP but lacks the check for this assumption. Granger causality (GC) — a method of assessing causal interactions between time series data — is gaining popularity in neurosciences. In our work, we used ABP and ICP data recorded at the frequency of 100 Hz or higher from 235 traumatic brain injury patients. We focused on time domain GC. Analysis was first performed directly on high-resolution data, which included pulse waves. We showed that due to the measurement delay in high-resolution ABP data, GC analysis may erroneously indicate strong ICP→ABP causal relation. Subsequently, the data were downsampled to 0.1 Hz, effectively removing pulse and respiratory waves. We aimed to investigate how different ways of calculating GC influence results and which way should be recommended for ABP-ICP recordings. We considered aspects like selecting autoregressive model order and dealing with data non-stationarity. In addition, we generated simulated signals to investigate the influence of gaps and different procedures of missing data imputation on GC estimation. We showed that unlike methods which interpolate missing data, replacing missing data by white Gaussian noise did not increase the rate of false GC detection. Python source code used in this study is available at: https://github.com/m-m-placek/python-icmplus-granger-causality. Statement of significanceAssessing causality between time series data is of particular interest when neuromonitoring indices are derived from those time series and causal interaction between them is assumed. Causality assessment can improve reliability of such indices and open pathways for their safe clinical implementation. Granger Causality (GC) has recently been investigated in data collected from traumatic brain injury patients. However, there are two main issues related to applications suggested in these studies. Firstly, they considered GC for entire multi-day data recordings or for 24-h long episodes. There is interest in considering causal relationships in finer granularity, also in terms of their potential real-time applications at the bedside. Secondly, GC calculation requires selecting some parameters and there is no unique nor standardised way of doing that. Many papers often provide very brief description of data pre-processing and GC calculation. For this reason, it can be harder to reproduce and compare results derived from GC application. Different ways of obtaining GC may potentially lead to inconsistent results. Here, we attempted to explore possibility of time-varying GC of finer granularity and to provide general guidelines for application of GC to neurocritical care time series affected by periods of missing values.

The link between financial stress index and economic activity: prominent Granger causalities across frequencies in Luxembourg

PurposeIn spite of the certain risk imposed by financial stress on the real economy, the relationship between financial stress and economic activity is complicated and underresearched, meaning that important gaps still remain in the authors’ understanding of this critical relationship. Therefore, the current study aims to answer the significant question regarding whether a stressful financial sector has predictive power on the real sector and vice versa. Hence, the study examines the causal interrelationship between financial stress index (FSI) and economic activity in Luxembourg as a sample country.Design/methodology/approachIn this study, accompanying the time domain Granger causality framework of Hacker and Hatemi-J (2012), the authors utilize the spectral causality technique of Breitung and Candelon (2006), which is based on the study of Geweke (1982) and Hosoya (1991). This method enables the researcher to measure the degree of a particular variation in time series. Moreover, it allows considering the nonlinearities and causality cycles. The authors further apply the recent method of Farné and Montanari (2018) that is a bootstrap framework on Granger-causality spectra, which allows for disambiguation in causalities.FindingsThe time-domain approach finds evidence of bidirectional causation between the variables. However, the spectral causality results indicate the causal linkages between the series are only valid under the medium-run frequency. This study’s findings emphasize covering the frequency causality to deliver a more comprehensive picture of the interrelationship between the variables.Originality/valueThere are many studies in this area that examine the nexus between financial stress and economic activity. However, the authors believe this paper is the first study in the context of Luxemburg. The authors focus on this country since its financial sector is designated as the most important pillar for the economy. Thus, a careful and reliable examination of the relationship between the financial sector and economic activity is likely to be of considerable interest to policymakers and researchers in this field.

Financial and economic development link in transitional economies: a spectral Granger causality analysis 1991?2017

Research background: The relationship between financial development and economic growth has been attracting attention in the field of economics since the times of the ?great moderation?. Previous empirical studies still fail to put forward a general conclusion on whether and how financial development affects economic growth. This is particularly true due to the lack of empirical research on the matter in question for countries in transition.
 Purpose of the article: This study aims to contribute to bridging the gap in the financial development-growth nexus in transitional economies. Understanding the mechanism behind financial development and economic growth should assist policymakers in the design of efficient economic policies or avoiding/alleviating financial cycles.
 Methods: Using Granger causality test in frequency domain, which shows to have more power over standard time domain Granger causality test, as well as gross domestic product (GDP) and the monetary base (M2 ? intermediate money), we investigated the finance-growth relationship in 19 Central, East, and Southeast European countries (CESEE) from 1991 to 2017.
 Findings & Value added: Study results show that financial development is important for growth in CESEE countries, thus supporting the ?supply-leading? theories in general for countries in the sample. Our findings indicate that the relationship between financial development and economic growth exists in CESEE countries (with one exception ? the Czech Republic) ranging from unidirectional (Albania, Bosnia and Hercegovina, Belarus, Estonia, Macedonia, Russia, Turkey), to bi-directional spectral Granger causality (Bulgaria, Croatia, Hungary, Kazakhstan, Latvia, Lithuania, Poland, Romania, Slovenia, Slovakia, Ukraine).

Renewable and non-renewable electricity consumption–economic growth nexus: Evidence from OECD countries

In this study, the relationship between renewable and non-renewable electricity consumption and economic growth was examined using data from the 1980–2015 period for 26 OECD countries. The relationship between the variables was examined using two different panel causality approaches in order to make a comparison. Time domain Granger causality tests cannot examine the causality relation at different frequencies. However, frequency domain Granger causality tests examine the causality at different frequencies. While Dumitrescu-Hurlin (2012) panel causality test is time domain causality test, the causality test developed by Croux and Reusens (2013) is the frequency domain causality test. According to the Dumitrescu-Hurlin panel causality test results, bidirectional causality has been determined between non-renewable electricity consumption and economic growth. On the contrary, the Croux and Reusens test results show that there is a bidirectional temporary, and permanent causality between economic growth and renewable-non-renewable electricity consumption. According to this results, for 26 OECD countries, where the feedback hypothesis is valid, policies need to be assessed not only in terms of economic growth, but also in terms of improving electricity energy supply security and environmental quality. Finally, policy-makers should promote the renewable electricity consumption to ensure energy security, reduce energy dependence, and encourage economic growth.

Does the SARB respond to oil price movements? Historical evidence from the frequency domain

ABSTRACTCausality testing procedures in the frequency domain and the time domain are employed to analyses the relationship between oil prices and interest rate in South Africa, covering the time period January 1936–November 2013 . Results show that the time domain Granger causality test fails to reject the null hypothesis for the full sample, and the test rejects the null hypothesis for the 3rd subsample (December 1998–November 2013), following structural break tests. Results for the frequency domain causality test show that for both of these samples the null hypothesis is rejected at certain frequencies: at higher frequencies for the full sample and at lower frequencies for the 3rd sample. With the majority of the 3rd subsample period coinciding with the inflation targeting regime, results highlight that the South African Reserve Bank (SARB) seems to have systematically responded to oil price shocks.

Critical Comments on EEG Sensor Space Dynamical Connectivity Analysis.

Many different analysis techniques have been developed and applied to EEG recordings that allow one to investigate how different brain areas interact. One particular class of methods, based on the linear parametric representation of multiple interacting time series, is widely used to study causal connectivity in the brain. However, the results obtained by these methods should be interpreted with great care. The goal of this paper is to show, both theoretically and using simulations, that results obtained by applying causal connectivity measures on the sensor (scalp) time series do not allow interpretation in terms of interacting brain sources. This is because (1) the channel locations cannot be seen as an approximation of a source's anatomical location and (2) spurious connectivity can occur between sensors. Although many measures of causal connectivity derived from EEG sensor time series are affected by the latter, here we will focus on the well-known time domain index of Granger causality (GC) and on the frequency domain directed transfer function (DTF). Using the state-space framework and designing two simulation studies we show that mixing effects caused by volume conduction can lead to spurious connections, detected either by time domain GC or by DTF. Therefore, GC/DTF causal connectivity measures should be computed at the source level, or derived within analysis frameworks that model the effects of volume conduction. Since mixing effects can also occur in the source space, it is advised to combine source space analysis with connectivity measures that are robust to mixing.

Does sunspot numbers cause global temperatures? A reconsideration using non-parametric causality tests

Abstract In a recent paper, Gupta et al., (2015), analyzed whether sunspot numbers cause global temperatures based on monthly data covering the period 1880:1–2013:9. The authors find that standard time domain Granger causality test fails to reject the null hypothesis that sunspot numbers do not cause global temperatures for both full and sub-samples, namely 1880:1–1936:2, ​1936:3–1986:11 and 1986:12–2013:9 (identified based on tests of structural breaks). However, frequency domain causality test detects predictability for the full-sample at short (2–2.6 months) cycle lengths, but not the sub-samples. But since, full-sample causality cannot be relied upon due to structural breaks, Gupta et al., (2015) conclude that the evidence of causality running from sunspot numbers to global temperatures is weak and inconclusive. Given the importance of the issue of global warming, our current paper aims to revisit this issue of whether sunspot numbers cause global temperatures, using the same data set and sub-samples used by Gupta et al., (2015), based on an nonparametric Singular Spectrum Analysis (SSA)-based causality test. Based on this test, we however, show that sunspot numbers have predictive ability for global temperatures for the three sub-samples, over and above the full-sample. Thus, generally speaking, our non-parametric SSA-based causality test outperformed both time domain and frequency domain causality tests and highlighted that sunspot numbers have always been important in predicting global temperatures.

Causality between energy poverty and economic growth in Africa: Evidences from time and frequency domain causality test

Due to the growing concern regarding energy poverty and its relation to economic growth, the paper evaluates the causality between both fields in Sub-Saharan Africa. The paper reviews all aggregated income levels thus developing aggregated series, from 1973 to 2012, in annual frequency. The well-established and generally accepted time domain Granger causality analysis is adopted. In addition, a new frequency domain causality test is performed enabling the identification and distinguishing of the causal relationship, while considering each specific frequency. Significant results are withdrawn from the time domain causality test indicating bi-directional causal links between economic growth and energy consumption, especially with regard to fossil fuel energy consumption. The comparisons between the frequency domain causality results, of different variables indicate not only a highly unidirectional causality relationship between energy consumption and economic growth, but also a tendency of enhanced significance for the emerging cycle length.

Significant feed-forward connectivity revealed by high frequency components of BOLD fMRI signals

Granger causality analysis has been suggested as a method of estimating causal modulation without specifying the direction of information flow a priori. Using BOLD-contrast functional MRI (fMRI) data, such analysis has been typically implemented in the time domain. In this study, we used magnetic resonance inverse imaging, a method of fast fMRI enabled by massively parallel detection allowing up to 10Hz sampling rate, to investigate the causal modulation at different frequencies up to 5Hz. Using a visuomotor two-choice reaction-time task, both the spectral decomposition of Granger causality and isolated effective coherence revealed that the BOLD signal at frequency up to 3Hz can still be used to estimate significant dominant directions of information flow consistent with results from the time-domain Granger causality analysis. We showed the specificity of estimated dominant directions of information flow at high frequencies by contrasting causality estimates using data collected during the visuomotor task and resting state. Our data suggest that hemodynamic responses carry physiological information related to inter-regional modulation at frequency higher than what has been commonly considered.

Do sunspot numbers cause global temperatures? Evidence from a frequency domain causality test

This article applies the causality test in the frequency domain, developed by Breitung and Candelon (2006), to analyse whether sunspot numbers (used as a partial approximation to solar irradiance) cause global temperatures, using monthly data covering the time period 1880:1–2013:9. While standard time domain Granger causality test fails to reject the null hypothesis that sunspot numbers do not cause global temperatures for both full and sub-samples (identified based on tests of structural breaks), the frequency domain causality test detects predictability for both the full-sample and the last sub-sample at short (2–2.6 months) and long (10.3 months and above) cycle lengths, respectively. Our results highlight the importance of analysing causality using the frequency domain test, which, unlike the time domain Granger causality test, allows us to decompose causality by different time horizons, and hence, could detect predictability at certain cycle lengths even when the time domain causality test might fail to pick up any causality. Further, given the widespread discussion in the literature, those results for the full-sample causality, irrespective of whether it is in time or frequency domains, cannot be relied upon when there are structural breaks present, and one needs to draw inference regarding causality from the sub-samples, we can conclude that there has been an emergence of causality running from sunspot numbers to global temperatures only recently at cycle length of 10.3 months and above.

Root cause diagnosis of plant-wide oscillations using Granger causality

Oscillations are common in closed-loop controlled processes which, once generated, can propagate along process flows and feedback paths of the whole plant. It is important to detect and diagnose such oscillations to maintain high control performance. This paper presents a new data-driven time series method for diagnosing the sources and propagation paths of plant-wide oscillations. The proposed method first uses a latent variable method to select features which carry significant common oscillations, then applies both time-domain Granger causality and spectral Granger causality to provide reliable diagnosis of oscillation sources and propagations. Simulation tests and an industrial case study are shown to demonstrate the effectiveness of the proposed method.

Lag-based effective connectivity applied to fMRI: A simulation study highlighting dependence on experimental parameters and formulation

A vast repertoire of methods is currently available to study effective brain connectivity based on neuroimaging data, among which lag-based measures can be distinguished. Although several studies have previously assessed the performance of such measures, their validity in different conditions remains unclear. In the current study, several lag-based effective connectivity measures are tested and benchmarked using simulated fMRI data, conceived to reflect a broad range of different situations with practical interest. The main goal is two-fold: 1) to provide a thorough overview of lag-based effective connectivity measures, and 2) to assess their performance in specific experimental conditions, thereby providing guidance for future effective connectivity studies involving fMRI. We focus on well-known lag-based measures, cover existing improvements and alternative formulations in some cases: Granger causality (GC), Geweke's Granger causality (GGC), directed transfer function (DTF), partial directed coherence (PDC), phase slope index (PSI), and transfer entropy (TE). Benchmarking consists in identifying causal relations in local field potential (LFP) networks that have their output convolved with a canonical hemodynamic response function (HRF) with varying node number, topology, coupling strength, neuronal delay, repetition time (TR), signal-to-noise ratio (SNR) and HRF variability. In a first set of simulations, we cover all possible combinations of discretized values of the previous variables, for networks with 2 and 3 nodes, and find that the measure with best performance (time-domain Granger Causality) is able to detect neuronal delays of a few hundreds of milliseconds with TRs between 0.25 and 2s and neuronal delays below 100ms for TRs that are also below 100ms, with more than 80% accuracy in realistic conditions. For networks with more than 3 nodes, we find that the number of nodes and the density of causal links degrade sensitivity, especially if the number of observations does not compensate for the increase in nodes, and that clustered networks can be more easily identified. In conclusion, this study argues in favor of the applicability of lag-based measures in the context of fMRI, provided that a stringent set of experimental specifications is met and that the chosen measure is applied with full knowledge of its limitations and specific constraints.

Cardiovascular control and time domain Granger causality: insights from selective autonomic blockade

We studied causal relations among heart period (HP), systolic arterial pressure (SAP) and respiration (R) according to the definition of Granger causality in the time domain. Autonomic pharmacological challenges were used to alter the complexity of cardiovascular control. Atropine (AT), propranolol and clonidine (CL) were administered to block muscarinic receptors, β-adrenergic receptors and centrally sympathetic outflow, respectively. We found that: (i) at baseline, HP and SAP interacted in a closed loop with a dominant causal direction from HP to SAP; (ii) pharmacological blockades did not alter the bidirectional closed-loop interactions between HP and SAP, but AT reduced the dominance of the causal direction from HP to SAP; (iii) at baseline, bidirectional interactions between HP and R were frequently found; (iv) the closed-loop relation between HP and R was unmodified by the administration of drugs; (v) at baseline, unidirectional interactions from R to SAP were often found; and (vi)while AT induced frequently an uncoupling between R and SAP, CL favoured bidirectional interactions. These results prove that time domain measures of Granger causality can contribute to the description of cardiovascular control by suggesting the temporal direction of the interactions and by separating different causality schemes (e.g. closed loop versus unidirectional relations).

More discussions for granger causality and new causality measures

Granger causality (GC) has been widely applied in economics and neuroscience to reveal causality influence of time series. In our previous paper (Hu etal., in IEEE Trans on Neural Netw, 22(6), pp. 829-844, 2011), we proposed new causalities in time and frequency domains and particularly focused on new causality in frequency domain by pointing out the shortcomings/limitations of GC or Granger-alike causality metrics and the advantages of new causality. In this paper we continue our previous discussions and focus on new causality and GC or Granger-alike causality metrics in time domain. Although one strong motivation was introduced in our previous paper (Hu etal., in IEEE Trans on Neural Netw, 22(6), pp. 829-844, 2011) we here present additional motivation for the proposed new causality metric and restate the previous motivation for completeness. We point out one property of conditional GC in time domain and the shortcomings/limitations of conditional GC which cannot reveal the real strength of the directional causality among three time series. We also show the shortcomings/limitations of directed causality (DC) or normalize DC for multivariate time series and demonstrate it cannot reveal real causality at all. By calculating GC and new causality values for an example we demonstrate the influence of one of the time series on the other is linearly increased as the coupling strength is linearly increased. This fact further supports reasonability of new causality metric. We point out that larger instantaneous correlation does not necessarily mean larger true causality (e.g., GC and new causality), or vice versa. Finally we conduct analysis of statistical test for significance and asymptotic distribution property of new causality metric by illustrative examples.

Causality Analysis of Neural Connectivity: Critical Examination of Existing Methods and Advances of New Methods

Granger causality (GC) is one of the most popular measures to reveal causality influence of time series and has been widely applied in economics and neuroscience. Especially, its counterpart in frequency domain, spectral GC, as well as other Granger-like causality measures have recently been applied to study causal interactions between brain areas in different frequency ranges during cognitive and perceptual tasks. In this paper, we show that: 1) GC in time domain cannot correctly determine how strongly one time series influences the other when there is directional causality between two time series, and 2) spectral GC and other Granger-like causality measures have inherent shortcomings and/or limitations because of the use of the transfer function (or its inverse matrix) and partial information of the linear regression model. On the other hand, we propose two novel causality measures (in time and frequency domains) for the linear regression model, called new causality and new spectral causality, respectively, which are more reasonable and understandable than GC or Granger-like measures. Especially, from one simple example, we point out that, in time domain, both new causality and GC adopt the concept of proportion, but they are defined on two different equations where one equation (for GC) is only part of the other (for new causality), thus the new causality is a natural extension of GC and has a sound conceptual/theoretical basis, and GC is not the desired causal influence at all. By several examples, we confirm that new causality measures have distinct advantages over GC or Granger-like measures. Finally, we conduct event-related potential causality analysis for a subject with intracranial depth electrodes undergoing evaluation for epilepsy surgery, and show that, in the frequency domain, all measures reveal significant directional event-related causality, but the result from new spectral causality is consistent with event-related time-frequency power spectrum activity. The spectral GC as well as other Granger-like measures are shown to generate misleading results. The proposed new causality measures may have wide potential applications in economics and neuroscience.

Point:Counterpoint: Respiratory sinus arrhythmia is due to a central mechanism vs. respiratory sinus arrhythmia is due to the baroreflex mechanism

Blood pressure and heart periods fluctuate at respiratory frequencies in healthy humans. Some researchers ([8][1], [23][2]) explain this as a cause-and-effect relation: blood pressure changes trigger baroreflex-mediated R-R interval changes. Here I make the case that respiratory sinus arrhythmia is