Non-linear Granger Causality Methods Research Articles

Downside and upside risk spillovers between financial industry and real economy based on linear and nonlinear networks

The spillover effects between financial sectors and real economy in different risk levels are of concern for investors and regulatory authorities. Firstly, based on the sector returns of China, the VaRs at different quantiles are estimated by MVMQ-CAViaR model. Then, we construct linear and nonlinear risk spillover networks in downside, normal and upside cases by employing DY and nonlinear Granger causality methods. Finally, we analyze topological characteristics of linear and nonlinear risk spillover networks at the system and sector levels. The results show that linear and nonlinear risk spillover networks in different risk levels exhibit various topology properties, they are unevenly spread over each risk level. At the system-level, we observe that there is a significant difference between linear and nonlinear risk spillover networks in uniqueness and overlapping. At the sector-level, the financial sectors (such as DF and RE sectors) can form a certain spillover effect on sectors of real economy across quantiles, but the net spillover effects of the financial sectors are smaller than that of some real economy sectors. Finally, the crisis shocks have impact on risk spillover effects between financial sectors and real economy. In downside and upside cases, the spillover effects between sectors during crisis period is higher than that during pre-crisis period.

Neural Granger Causality.

While most classical approaches to Granger causality detection assume linear dynamics, many interactions in real-world applications, like neuroscience and genomics, are inherently nonlinear. In these cases, using linear models may lead to inconsistent estimation of Granger causal interactions. We propose a class of nonlinear methods by applying structured multilayer perceptrons (MLPs) or recurrent neural networks (RNNs) combined with sparsity-inducing penalties on the weights. By encouraging specific sets of weights to be zero-in particular, through the use of convex group-lasso penalties-we can extract the Granger causal structure. To further contrast with traditional approaches, our framework naturally enables us to efficiently capture long-range dependencies between series either via our RNNs or through an automatic lag selection in the MLP. We show that our neural Granger causality methods outperform state-of-the-art nonlinear Granger causality methods on the DREAM3 challenge data. This data consists of nonlinear gene expression and regulation time courses with only a limited number of time points. The successes we show in this challenging dataset provide a powerful example of how deep learning can be useful in cases that go beyond prediction on large datasets. We likewise illustrate our methods in detecting nonlinear interactions in a human motion capture dataset.

Identifying the pulsed neuron networks\u2019 structures by a nonlinear Granger causality method

BackgroundIt is a crucial task of brain science researches to explore functional connective maps of Biological Neural Networks (BNN). The maps help to deeply study the dominant relationship between the structures of the BNNs and their network functions.ResultsIn this study, the ideas of linear Granger causality modeling and causality identification are extended to those of nonlinear Granger causality modeling and network structure identification. We employed Radial Basis Functions to fit the nonlinear multivariate dynamical responses of BNNs with neuronal pulse firing. By introducing the contributions from presynaptic neurons and detecting whether the predictions for postsynaptic neurons’ pulse firing signals are improved or not, we can reveal the information flows distribution of BNNs. Thus, the functional connections from presynaptic neurons can be identified from the obtained network information flows. To verify the effectiveness of the proposed method, the Nonlinear Granger Causality Identification Method (NGCIM) is applied to the network structure discovery processes of Spiking Neural Networks (SNN). SNN is a simulation model based on an Integrate-and-Fire mechanism. By network simulations, the multi-channel neuronal pulse sequence data of the SNNs can be used to reversely identify the synaptic connections and strengths of the SNNs.ConclusionsThe identification results show: for 2–6 nodes small-scale neural networks, 20 nodes medium-scale neural networks, and 100 nodes large-scale neural networks, the identification accuracy of NGCIM with the Gaussian kernel function was 100%, 99.64%, 98.64%, 98.37%, 98.31%, 84.87% and 80.56%, respectively. The identification accuracies were significantly higher than those of a traditional Linear Granger Causality Identification Method with the same network sizes. Thus, with an accumulation of the data obtained by the existing measurement methods, such as Electroencephalography, functional Magnetic Resonance Imaging, and Multi-Electrode Array, the NGCIM can be a promising network modeling method to infer the functional connective maps of BNNs.

On the performance of temporal Granger causality measurements on time series: a comparative study

Nowadays, Granger causality techniques are frequently applied to investigate complex dynamical systems such as brain networks. Indeed, various derivations have been proposed from the initially basic definition of the Granger causality concept to deal with two fundamental issues of how to cope with dynamical nonlinearities when they are present and how to prevent model over fitting, i.e., how to eliminate nonsignificant regressors. In this paper, a comparative study is conducted on four methods facing differently these issues, namely the multivariate linear Granger causality, the kernel Granger causality, the restricted Granger causality and the nonlinear Granger causality, the latter relying on the nonlinear Wavelet Network vectorial autoregressive model. For an objective comparison of these methods, a new strategy is proposed to derive linear and nonlinear partial model orders to be applied, respectively, to the multivariate linear Granger causality and the nonlinear Granger causality methods which generally use a global model order.

A Linear and Non-Linear Causality Analysis between Military Expenditures and External Debt in NATO Member Countries

This paper deploys the linear and non-linear Granger causality methods in order to determine the causal relationship between military expenditures and external debt in NATO countries for the time period 1960-2015. Its innovative feature lies in the empirical application of the Francis et al. (2010) nonlinear causality test. To our knowledge, this is the first study to employ the specific test in order to explore the existence of potential nonlinear links between military spending and debt. The empirical results indicate the existence of linearity in the cases of Greece, Italy, UK and USA and the existence of nonlinearity in the cases of Turkey and USA. The paper aims to provide valuable input to the regulators and decision makers.

Changes in corticocortical and corticohippocampal network during absence seizures in WAG/Rij rats revealed with time varying Granger causality.

Spike-and-wave discharges (SWDs) recorded in the cortical EEGs of WAG/Rij rats are the hallmark for absence epilepsy in this model. Although this type of epilepsy was long regarded as a form of primary generalized epilepsy, it is now recognized that there is an initiation zone - the perioral region of the somatosensory cortex. However, networks involved in spreading the seizure are not yet fully known. Previously, the dynamics of coupling between different layers of the perioral cortical region and between these zones and different thalamic nuclei was studied in time windows around the SWDs, using nonlinear Granger causality. The aim of the present study was to investigate, using the same method, the coupling dynamics between different regions of the cortex and between these regions and the hippocampus. Local field potentials were recorded in the frontal, parietal, and occipital cortices and in the hippocampus of 19 WAG/Rij rats. To detect changes in coupling reliably in a short time window, in order to provide a good temporal resolution, the innovative adapted time varying nonlinear Granger causality method was used. Mutual information function was calculated in addition to validate outcomes. Results of both approaches were tested for significance. The SWD initiation process was revealed as an increase in intracortical interactions starting from 3.5s before the onset of electrographic seizure. The earliest preictal increase in coupling was directed from the frontal cortex to the parietal cortex. Then, the coupling became bidirectional, followed by the involvement of the occipital cortex (1.5s before SWD onset). There was no driving from any cortical region to hippocampus, but a slight increase in coupling from hippocampus to the frontoparietal cortex was observed just before SWD onset. After SWD onset, an abrupt drop in coupling in all studied pairs was observed. In most of the pairs, the decoupling rapidly disappeared, but driving force from hippocampus and occipital cortex to the frontoparietal cortex was reduced until the SWD termination. Involvement of multiple cortical regions in SWD initiation shows the fundamental role of corticocortical feedback loops, forming coupling architecture and triggering the generalized seizure. The results add to the ultimate aim to construct a complete picture of brain interactions preceding and accompanying absence seizures in rats.

Non-Linear Analysis of Post Keynesian Phillips Curve in Canada Labor Market

Abstract This paper aims to analyze Post-Keynesian Phillips Curve by using non-linear ARDL approach and non-linear Granger causality method for the period from 1957 to 2015 in Canada. This study is differed from other empirical paper by using non-linear ARDL method which determined there is long-run asymmetric relationship between the selected macroeconomic variables for Canada. Canada exhibits bi-directional causality relationship between inflation-unemployment, unemployment-economic growth and inflation-economic growth which refers that the country has flexible labor market.

The Chaotic Relationship between Oil Return, Gold, Silver and Copper Returns in TURKEY: Non-Linear ARDL and Augmented Non-linear Granger Causality

The structure of the relationship between oil prices, gold price, silver price and copper price are not only important for economists but also for policymakers since it contributes to the policy debate on the link between variables and co-movement of the variables. In this paper, the relationship between oil prices and the price of gold and silver was analysed by BDS test, non-linear ARDL approach and two non-linear Granger causality methods for 1973:1 – 2012:11 period in Turkey. This study complements previous empirical papers. However, it differs from the existing literature with simultaneous use of nonlinear ARDL and two non-linear causality model: Hiemstra and Jones (1994) non-linear causality and augmented granger causality developed by this paper. The main findings of this paper are: (a) the gold price level showed positive asymmetric response to changes in the oil price in the short-- and long-run. The gold price probably possesses some market power and it is a means of store of value. Because of the exception of gold, there is a substantial sluggishness in the adaption to changes in demand. In the long run the exception of gold lags and adjustment costs should play a smaller part; b) there is a unique long-term relationship between oil prices and the prices of gold, silver and cooper; and (c) there is a unidirectional Granger causality between oil price and precious metal price.

Оптимальный подбор параметров прогностических моделей в методе нелинейной причинности по Грейнджеру в приложении к сигналам, характеризуемым хорошо выраженными временными масштабами

Оптимальный подбор параметров прогностических моделей в методе нелинейной причинности по Грейнджеру в приложении к сигналам, характеризуемым хорошо выраженными временными масштабами

Evidence For Non-Linear Causality Between Public Spending And Income In The European Union Countries

<p class="MsoSubtitle" style="text-align: justify; margin: 0in 0.5in 0pt;"><span style="font-family: Times New Roman;"><span style="color: black; font-size: 10pt; font-weight: normal; text-decoration: none; text-underline: none;">This paper deploys the non-linear Granger causality methods in order to determine the causal relationship between national income and government expenditure in the European Union countries over the post-war time period. For this purpose, six alternative functional forms of Wagner’s law have been adopted. The empirical results </span><span style="font-size: 10pt; font-weight: normal; text-decoration: none; text-underline: none;">indicate support for non-linear causality between income and government expenditure and they may prove useful theoretical and empirical research for the regulators and the policy makers. </span></span></p>