Granger Causality Inference Research Articles

Granger Causal Inference Based on Dual Laplacian Distribution and Its Application to MI-BCI Classification.

Granger causality-based effective brain connectivity provides a powerful tool to probe the neural mechanism for information processing and the potential features for brain computer interfaces. However, in real applications, traditional Granger causality is prone to the influence of outliers, such as inevitable ocular artifacts, resulting in unreasonable brain linkages and the failure to decipher inherent cognition states. In this work, motivated by constructing the sparse causality brain networks under the strong physiological outlier noise conditions, we proposed a dual Laplacian Granger causality analysis (DLap-GCA) by imposing Laplacian distributions on both model parameters and residuals. In essence, the first Laplacian assumption on residuals will resist the influence of outliers in electroencephalogram (EEG) on causality inference, and the second Laplacian assumption on model parameters will sparsely characterize the intrinsic interactions among multiple brain regions. Through simulation study, we quantitatively verified its effectiveness in suppressing the influence of complex outliers, the stable capacity for model estimation, and sparse network inference. The application to motor-imagery (MI) EEG further reveals that our method can effectively capture the inherent hemispheric lateralization of MI tasks with sparse patterns even under strong noise conditions. The MI classification based on the network features derived from the proposed approach shows higher accuracy than other existing traditional approaches, which is attributed to the discriminative network structures being captured in a timely manner by DLap-GCA even under the single-trial online condition. Basically, these results consistently show its robustness to the influence of complex outliers and the capability of characterizing representative brain networks for cognition information processing, which has the potential to offer reliable network structures for both cognitive studies and future brain-computer interface (BCI) realization.

The making-or-breaking of material and resource efficiency in the Nordics

The relevance of efficient direct material input through both export market and domestic material sources offers useful material and resource productivity guidelines from both economic and environmental sustainability dimensions. In the current context, the drivers of material and resource efficiency in the Nordic region are examined by utilizing requisite empirical approaches over the period 1995–2020. The investigation revealed that economic activities which are characterized by Gross domestic product (GDP) alongside the growth of urban population and utilization of oil energy are all detrimental to the region's resource efficiency. It implies that material utilization efficiency cannot be optimized with the current trend of the region's GDP, urban population growth and the use of dirty energy. Contrarily, the findings, further revealed that alternative energy utilization vis-à-vis renewables are key indicators to spur material and resource efficiency in the region, thus throwing more support for the region's unavoidable energy transition goal. These highlighted results alongside the Granger causality inference offer sustainable development measures that are specifically motivated through the improvement of efficient and optimization of output.

Fiscal Policy, Oil Price, Foreign Direct Investment, and Renewable Energy—A Path to Sustainable Development in South Africa

Since South Africa is in pursuit of accomplishing the 2030 Sustainable Development Goals, it has become pertinent to accelerate the desired energy transition. Against this background, this work aims to evaluate the effects of oil prices, fiscal policy, and foreign direct investment on renewable energy consumption in South Africa from 1979 to 2019. Using the novel Augmented Autoregressive Distributed Lag approach, this study finds that economic growth and taxation revenues positively promote renewable energy in South Africa. In contrast, the findings show that an increase in oil prices has a negative impact on renewable energy in both short and long periods. Likewise, the research shows that foreign direct investment was not found to enhance renewable energy. The findings from fully modified-OLS, dynamic ordinary least squares, and canonical cointegrating regression models corroborate the findings of the Autoregressive Distributed Lag method. For the Granger causality inference, the findings demonstrate that there is a one-way causal connection detected from economic growth to the consumption of renewable energy. Based on these outcomes, a policy framework has been offered to help South Africa to attain the sustainable development goals.

Can green resource productivity, renewable energy, and economic globalization drive the pursuit of carbon neutrality in the top energy transition economies?

ABSTRACT This research explores the role of green resource productivity, renewable energy, economic globalization, and economic growth towards advancing the pursuits of decarbonization in top energy transition economies. This study achieves this objective by adopting both asymmetric and symmetric econometric methods for the period between 1990 and 2021. This study adopted the Method of Moments Quantile Regression (MMQR) to uncover the asymmetric effect of the regressors on carbon emissions. The MMQR results suggest that in all quantiles, green resource productivity, renewable energy, and economic globalization mitigate CO2 emissions, while economic growth induces CO2 emissions. Additionally, for the robustness analysis, we disaggregated economic globalization into trade and financial globalization and investigated their roles towards achieving decarbonization. We uncovered that financial globalization mitigates CO2 emissions at all quantiles, but at the lower and middle quantiles, trade globalization mitigates CO2 emissions. Moreover, for the symmetric estimation, the following estimators: Fixed effect Ordinary Least Square, Fully Modified Ordinary Least Square, and Dynamic Ordinary Least Square estimators were employed in this study. Their outcome corroborated the findings of this MMQR. For the Granger causality inference, the outcome suggests that there is a bi-directional causality between renewable energy and CO2 emissions. Furthermore, we find a feedback causality association between financial globalization and CO2 emissions, and a one-way causal interconnection is detected from CO2 emissions to trade globalization. Moreover, we detected that there is a causal association flowing from economic globalization to CO2 emissions. Finally, an unidirectional causal interaction is detected from economic growth to CO2 emissions. Consequently, the research’s findings provide applicable policy.

A Multi-Factor Selection and Fusion Method through the CNN-LSTM Network for Dynamic Price Forecasting

Commodity prices are important factors for investment management and policy-making, and price forecasting can help in making better business decisions. Due to the complex and volatile nature of the market, commodity prices tend to change frequently and fluctuate violently, often influenced by many potential factors with strong nonstationary and nonlinear characteristics. Thus, it is difficult to obtain satisfactory prediction effects by only using the historical data of prices individually. To address this problem, a novel dynamic price forecasting method based on multi-factor selection and fusion with CNN-LSTM is proposed. First, the factors related to commodity price are collected, and Granger causality inference is used to identify causal factors that affect the commodity price. Then, XGBoost is used to evaluate the importance of the remaining factors and screen out critical factors to reduce the interference of redundant information. Due to the high amount and complicated changes of the selected factors, a convolutional neural network is employed to fuse the selected factors and extract the hidden features. Finally, a long short-term memory network is adopted to establish a multi-input predictor to obtain the dynamic price. Compared with several advanced approaches, the evaluation results indicate that the proposed method has an excellent performance in dynamic price forecasting.

Anthropogenic Contributions to the 2021 Pacific Northwest Heatwave

AbstractDaily maximum temperatures during the 2021 heatwave in the Pacific Northwest United States and Canada shattered century old records. Multiple causal factors, including anthropogenic climate change, contributed to these high temperatures, challenging traditional methods of attributing human influence. We demonstrate that the observed 2021 daily maximum temperatures are far above the bounds of Generalized Extreme Value distributions fitted from historical data. Hence, confidence in Granger causal inference statements about the human influence on this heatwave is low. Alternatively, we present a more conditional hindcast attribution study using two regional models. We performed ensembles of simulations of the heatwave to investigate how the event would have changed if it had occurred without anthropogenic climate change and with future warming. We found that global warming caused a ∼0.8°C–1°C increase in heatwave temperatures. Future warming would lead to a ∼5°C increase in heatwave temperature by the end of the 21st century.

Are green resource productivity and environmental technologies the face of environmental sustainability in the Nordic region?

AbstractThis study examines whether the raw material productivity, export intensification, and environmental‐related technologies in the Nordic region (i.e., Denmark, Finland, Iceland, Norway, and Sweden) drives the region's carbon neutrality target. By adopting both symmetric and asymmetric empirical approaches over the period 1990–2019, the study found that positive and negative shifts in environmental‐related technologies mitigates greenhouse gas (GHG) emissions in the region with the former causing a larger impact. Furthermore, the findings reveal that a positive shift in raw material productivity mitigates GHG emissions while a negative shift in raw material productivity causes a surge in GHG emissions especially in the long‐run. Moreover, a positive (negative) shift in export intensity yields a decline (upsurge) in GHG emissions in the long‐run. In the symmetric framework, in both long‐ and short‐run, the result reveals that economic growth upsurges GHG emissions while raw material productivity for green growth and environmental‐related technologies mitigates GHG emissions. This demonstrates the efficient raw material productivity profile of the Nordic countries. Alongside the Granger causality inference, the result further informs that energy intensity is crucial to curbing GHG emissions in the region. Thus, the result from the study offers relevant policy instructions.

Granger causality from quantized measurements

An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved. Assuming a partial finite-order Markov property, a characterization of Granger causality in terms of the rank of a matrix involving the covariances is presented. We call this the causality matrix. The smallest singular value of the causality matrix gives a lower bound on the distance between the two conditional Gaussian distributions appearing in the definition of Granger causality and yields a new measure of causality. Then, conditions are derived under which Granger causality between jointly Gaussian processes can be reliably inferred from the second order moments of quantized measurements. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through measurements quantized via non-uniform or high resolution quantizers. Apart from the assumed partial Markov order and joint Gaussianity, this approach does not require the parameters of a system model to be identified. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations. The effectiveness of the proposed method is illustrated by simulation results.

Granger-causal inference of the lamellipodial actin regulator hierarchy by live cell imaging without perturbation.

Many cell regulatory systems implicate nonlinearity and redundancy among components. The regulatory network governing lamellipodial and lamellar actin structures is prototypical of such a system, containing tens of actin-nucleating and -modulating molecules with functional overlap and feedback loops. Due to instantaneous and long-term compensation, phenotyping the system response to perturbation provides limited information on the roles the targeted component plays in the unperturbed system. Accordingly, how individual actin regulators contribute to lamellipodial dynamics remains ambiguous. Here, we present a perturbation-free reconstruction of cause-effect relations among actin regulators by applying Granger-causal inference to constitutive image fluctuations that indicate regulator recruitment as a proxy for activity. Our analysis identifies distinct zones of actin regulator activation and of causal effects on filament assembly and delineates actin-dependent and actin-independent regulator roles in controlling edge motion. We propose that edge motion is driven by assembly of two independently operating actin filament systems.

Broadcasting of amplitude- and frequency-modulated c-di-GMP signals facilitates cooperative surface commitment in bacterial lineages

Work on surface sensing in bacterial biofilms has focused on how cells transduce sensory input into cyclic diguanylate (c-di-GMP) signaling, low and high levels of which generally correlate with high-motility planktonic cells and low-motility biofilm cells, respectively. Using Granger causal inference methods, however, we find that single-cell c-di-GMP increases are not sufficient to imply surface commitment. Tracking entire lineages of cells from the progenitor cell onward reveals that c-di-GMP levels can exhibit increases but also undergo oscillations that can propagate across 10 to 20 generations, thereby encoding more complex instructions for community behavior. Principal component and factor analysis of lineage c-di-GMP data shows that surface commitment behavior correlates with three statistically independent composite features, which roughly correspond to mean c-di-GMP levels, c-di-GMP oscillation period, and surface motility. Surface commitment in young biofilms does not correlate to c-di-GMP increases alone but also to the emergence of high-frequency and small-amplitude modulation of elevated c-di-GMP signal along a lineage of cells. Using this framework, we dissect how increasing or decreasing signal transduction from wild-type levels, by varying the interaction strength between PilO, a component of a principal surface sensing appendage system, and SadC, a key hub diguanylate cyclase that synthesizes c-di-GMP, impacts frequency and amplitude modulation of c-di-GMP signals and cooperative surface commitment.

Granger-Causality Inference of the Existence of Unobserved Important Components in Network Analysis.

Detecting causal interrelationships in multivariate systems, in terms of the Granger-causality concept, is of major interest for applications in many fields. Analyzing all the relevant components of a system is almost impossible, which contrasts with the concept of Granger causality. Not observing some components might, in turn, lead to misleading results, particularly if the missing components are the most influential and important in the system under investigation. In networks, the importance of a node depends on the number of nodes connected to this node. The degree of centrality is the most commonly used measure to identify important nodes in networks. There are two kinds of degree centrality, which are in-degree and out-degree. This manuscrpt is concerned with finding the highest out-degree among nodes to identify the most influential nodes. Inferring the existence of unobserved important components is critical in many multivariate interacting systems. The implications of such a situation are discussed in the Granger-causality framework. To this end, two of the most recent Granger-causality techniques, renormalized partial directed coherence and directed partial correlation, were employed. They were then compared in terms of their performance according to the extent to which they can infer the existence of unobserved important components. Sub-network analysis was conducted to aid these two techniques in inferring the existence of unobserved important components, which is evidenced in the results. By comparing the results of the two conducted techniques, it can be asserted that renormalized partial coherence outperforms directed partial correlation in the inference of existing unobserved important components that have not been included in the analysis. This measure of Granger causality and sub-network analysis emphasizes their ubiquitous successful applicability in such cases of the existence of hidden unobserved important components.

Dense time-course gene expression profiling of the Drosophila melanogaster innate immune response

BackgroundImmune responses need to be initiated rapidly, and maintained as needed, to prevent establishment and growth of infections. At the same time, resources need to be balanced with other physiological processes. On the level of transcription, studies have shown that this balancing act is reflected in tight control of the initiation kinetics and shutdown dynamics of specific immune genes.ResultsTo investigate genome-wide expression dynamics and trade-offs after infection at a high temporal resolution, we performed an RNA-seq time course on D. melanogaster with 20 time points post Imd stimulation. A combination of methods, including spline fitting, cluster analysis, and Granger causality inference, allowed detailed dissection of expression profiles, lead-lag interactions, and functional annotation of genes through guilt-by-association. We identified Imd-responsive genes and co-expressed, less well characterized genes, with an immediate-early response and sustained up-regulation up to 5 days after stimulation. In contrast, stress response and Toll-responsive genes, among which were Bomanins, demonstrated early and transient responses. We further observed a strong trade-off with metabolic genes, which strikingly recovered to pre-infection levels before the immune response was fully resolved.ConclusionsThis high-dimensional dataset enabled the comprehensive study of immune response dynamics through the parallel application of multiple temporal data analysis methods. The well annotated data set should also serve as a useful resource for further investigation of the D. melanogaster innate immune response, and for the development of methods for analysis of a post-stress transcriptional response time-series at whole-genome scale.

Coupling the driving forces of urban CO2 emission in Shanghai with logarithmic mean Divisia index method and Granger causality inference

This paper investigates the potential indicators influencing CO2 emission in Shanghai during 1995–2017 by a combined method of logarithmic mean Divisia index method (LMDI) and Granger causality test for the purpose of strengthening the sustainability in dynamic perspectives. Firstly, we quantify the contributions of potentially influential factors of CO2 emission, and then a further analysis of different relationships between CO2 emission and the mainly potential factors are identified. The results show that the motor vehicle amount, the disposable personal income, the carbon intensity, and the urbanization rate are the top four driving forces of CO2 emission. The result of Granger causality test indicates that the motor vehicle amount has a bidirectional Granger causality relationship with CO2 emission in different lags, while the urbanization rate, per motor vehicle secondary industry, per secondary industry population, per residents’ income GDP support coefficient and the carbon intensity have a one-way Granger causality relationship with CO2 emission. Interestingly, it is found that the policy implementation or main events are closely related to the influential factors of CO2 emission. Thus, policy makers should not only continue to implement current related policies of reducing CO2 emission but also pay attention to the effect of great events of urban development.

Directionality of paper reviewing and publishing of a scientist: A Granger causality inference

Directionality of paper reviewing and publishing of a scientist: A Granger causality inference

On the relationship between download and citation counts: An introduction of Granger-causality inference

Studies on the relationship between the numbers of citations and downloads of scientific publications is beneficial for understanding the mechanism of citation patterns and research evaluation. However, seldom studies have considered directionality issues between downloads and citations or adopted a case-by-case time lag length between the download and citation time series of each individual publication. In this paper, we introduce the Granger-causal inference strategy to study the directionality between downloads and citations and set up the length of time lag between the time series for each case. By researching the publications on the Lancet, we find that publications have various directionality patterns, but highly cited publications tend to feature greater possibilities to have Granger causality. We apply a step-by-step manner to introduce the Granger-causal inference method to information science as four steps, namely conducting stationarity tests, determining time lag between time series, establishing cointegration test, and implementing Granger-causality inference. We hope that this method can be applied by future information scientists in their own research contexts.

Granger Causality of Gaussian Signals from Binary or Non-uniformly Quantized Measurements

This paper studies the assessment of Granger causality between jointly Gaussian signals from binary/non-uniformly quantized measurements. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through non-uniformly quantized measurements. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations.

DLI: A Deep Learning-Based Granger Causality Inference

Integrating autoencoder (AE), long short-term memory (LSTM), and convolutional neural network (CNN), we propose an interpretable deep learning architecture for Granger causality inference, named deep learning-based Granger causality inference (DLI). Two contributions of the proposed DLI are to reveal the Granger causality between the bitcoin price and S&P index and to forecast the bitcoin price and S&P index with a higher accuracy. Experimental results demonstrate that there is a bidirectional but asymmetric Granger causality between the bitcoin price and S&P index. And the DLI performs a superior prediction accuracy by integrating variables that have causalities with the target variable into the prediction process.

Multilayer network analysis of oil linkages

Summary This manuscript proposes a new approach for unveiling existing linkages within the international oil market across multiple driving factors beyond production. A multilayer, multicountry network is extracted through a novel Bayesian graphical vector autoregressive model, which allows for a more comprehensive, dynamic representation of the network linkages than do traditional or static pairwise Granger-causal inference approaches. Building on previous work, the layers of the network include country- and region-specific oil production levels and rigs, both through simultaneous and lagged temporal dependences among key factors, while controlling for oil prices and a world economic activity index. The proposed approach extracts relationships across all variables through a dynamic, cross-regional network. This approach is highly scalable and adjusts for time-evolving linkages. The model outcome is a set of time-varying graphical networks that unveil both static representations of world oil linkages and variations in microeconomic relationships both within and between oil producers. An example is provided, illustrating the evolution of intra- and inter-regional relationships for two major interconnected oil producers: the United States, with a regional decomposition of its production and rig deployment, and the Arabian Peninsula and key Middle Eastern producers, with a country-based decomposition of production and rig deployment, while controlling for oil prices and global economic indices. Production is less affected by concurrent changes in oil prices and the overall economy than rigs. However, production is a lagged driver for prices, rather than rigs, which indicates that the linkage between rigs and production may not be fully accounted for in the markets.

Dynamics as a cause for the nanoscale organization of the genome

ABSTRACT Chromatin ‘blobs’ were recently identified by live super-resolution imaging of labeled nucleosomes as pervasive but fleeting structural entities. However, the mechanisms leading to the formation of these blobs and their functional implications are unknown. We explore here whether causal relationships exist between parameters that characterize the chromatin blob dynamics and structure, by adapting a framework for spatio-temporal Granger-causality inference. Our analysis reveals that chromatin dynamics is a key determinant for both blob area and local density. Such causality, however, could be demonstrated only in 10–20% of the nucleus, suggesting that chromatin dynamics and structure at the nanometer scale are dominated by stochasticity. We show that the theory of active semiflexible polymers can be invoked to provide potential mechanisms leading to the organization of chromatin into blobs. Our results represent a first step toward elucidating the mechanisms that govern the dynamic and stochastic organization of chromatin in the cell nucleus.

Granger-causality inference in the presence of gaps: An equidistant missing-data problem for non-synchronous recorded time series data

The inference of causal interactions from incomplete data represents a major issue in many areas of applications. The incompleteness of data has different directions. The direction of interest in this manuscript is the collection of data whose measurements are sampled at equally spaced intervals with missing observations. This direction has two different scenarios: either for synchronously or non-synchronously recorded data. There are many known gap-filling techniques, however, each has its own limitations. In addition, the presence of gaps violates the underlying assumptions of the existing standard time series analysis techniques especially in the framework of Granger-causality concept, such as Directed Partial Correlation (DPC). This results in incorrect misleading conclusions about the inferred interaction structure. Therefore, the implications of applying the concept of Granger-causality based DPC are presented. To this end, a new extended methodology is proposed based on a specific shifting technique to overcome the shortcomings of the standard DPC technique. The proposed methodology provides an evidence that it is possible to infer the underlying causality structure even in the presence of gaps for non-synchronously recorded data. This manuscript presents the problem at hand for stock market time series analysis, as a case study.