Nonparametric Granger Causality Research Articles

A dynamic causal topic model for mining activities from complex videos

In this paper, a novel probabilistic topic model is proposed for mining activities from complex video surveillance scenes. In order to handle the temporal nature of the video data, we devise a dynamical causal topic model (DCTM) that can detect the latent topics and causal interactions between them. The model is based on the assumption that all temporal relationships between latent topics at neighboring time steps follow a noisy-OR distribution. And the parameter of the noisy-OR distribution is estimated by a data driven approach based on the idea of nonparametric Granger causality statistic. Furthermore, for convergence analysis during model learning process, the Kullback-Leibler between the prior and the posterior distributions is calculated. At last, using the causality matrix learned by DCTM, the total causal influence of each topic is measured. We evaluate the proposed model through experimentations on several challenging datasets and demonstrate that our model can identify the high influence activity in crowded scenes.

Causality patterns for Brent, WTI, and Argus oil prices

ABSTRACTCausality patterns are analysed for daily Brent, West Texas Intermediate (WTI), and Argus Sour Crude Index (Argus) oil prices, Argus is the reference price for exports from Saudi Arabia, Kuwait and Iraq. Nonparametric Granger causality testing uncovers bi-directional causal links between Brent and WTI prices at multiple lags. Unidirectional causality from both Brent to Argus and WTI to Argus is also documented. If the current Saudi Arabia attempt to increase market share is successful, variations in Argus prices may start preceding movements in Brent and WTI, also.

Bridging the Gap: Dynamic Causal Modeling and Granger Causality Analysis of Resting State Functional Magnetic Resonance Imaging.

Granger causality (GC) and dynamic causal modeling (DCM) are the two key approaches used to determine the directed interactions among brain areas. Recent discussions have provided a constructive account of the merits and demerits. GC, on one side, considers dependencies among measured responses, whereas DCM, on the other, models how neuronal activity in one brain area causes dynamics in another. In this study, our objective was to establish construct validity between GC and DCM in the context of resting state functional magnetic resonance imaging (fMRI). We first established the face validity of both approaches using simulated fMRI time series, with endogenous fluctuations in two nodes. Crucially, we tested both unidirectional and bidirectional connections between the two nodes to ensure that both approaches give veridical and consistent results, in terms of model comparison. We then applied both techniques to empirical data and examined their consistency in terms of the (quantitative) in-degree of key nodes of the default mode. Our simulation results suggested a (qualitative) consistency between GC and DCM. Furthermore, by applying nonparametric GC and stochastic DCM to resting-state fMRI data, we confirmed that both GC and DCM infer similar (quantitative) directionality between the posterior cingulate cortex (PCC), the medial prefrontal cortex, the left middle temporal cortex, and the left angular gyrus. These findings suggest that GC and DCM can be used to estimate directed functional and effective connectivity from fMRI measurements in a consistent manner.

Did Baltic stock markets offer diversification benefits during the recent financial turmoil? Novel evidence from a nonparametric causality-in-quantiles test

Motivated by financial liberalization investors seek for new investment opportunities through international portfolio diversification. To this end we explore any asymmetric causal relationship between developed European stock markets (Germany, France and UK) and emerging Baltic markets namely; Estonia, Latvia and Lithuania. Our analysis focuses on the period before and after countries’ EU accession and pre- and post the global financial crisis. For this purpose, both the standard parametric test for causality and a novel nonparametric test for causality-in-quantiles are employed. The results of both the parametric and nonparametric Granger causality test support a causal relationship in mean that runs from all of the major markets to the Baltic markets across both samples. The results imply the existence of significant nonlinear return and volatility spillover from European markets to Baltic markets. Policy implications for international investors are also discussed.

Granger causality analysis with nonuniform sampling and its application to pulse-coupled nonlinear dynamics.

The Granger causality (GC) analysis is an effective approach to infer causal relations for time series. However, for data obtained by uniform sampling (i.e., with an equal sampling time interval), it is known that GC can yield unreliable causal inference due to aliasing if the sampling rate is not sufficiently high. To solve this unreliability issue, we consider the nonuniform sampling scheme as it can mitigate against aliasing. By developing an unbiased estimation of power spectral density of nonuniformly sampled time series, we establish a framework of spectrum-based nonparametric GC analysis. Applying this framework to a general class of pulse-coupled nonlinear networks and utilizing some particular spectral structure possessed by these nonlinear network data, we demonstrate that, for such nonlinear networks with nonuniformly sampled data, reliable GC inference can be achieved at a low nonuniform mean sampling rate at which the traditional uniform sampling GC may lead to spurious causal inference.

On economic uncertainty, stock market predictability and nonlinear spillover effects

This paper uses a k-th order nonparametric Granger causality test to analyze whether firm-level, economic policy and macroeconomic uncertainty indicators predict movements in real stock returns and their volatility. Linear Granger causality tests show that whilst economic policy and macroeconomic uncertainty indices can predict stock returns, firm-level uncertainty measures possess no predictability. However, given the existence of structural breaks and inherent nonlinearities in the series, we employ a nonparametric causality methodology, as linear modeling leads to misspecifications thus the results cannot be considered reliable. The nonparametric test reveals that in fact no predictability can be observed for the various measures of uncertainty i.e., firm-level, macroeconomic and economic policy uncertainty, vis-à-vis real stock returns. In turn, a profound causal predictability is demonstrated for the volatility series, with the exception of firm-level uncertainty. Overall our results not only emphasize the role of economic and firm-level uncertainty measures in predicting the volatility of stock returns, but also presage against using linear models which are likely to suffer from misspecification in the presence of parameter instability and nonlinear spillover effects.

Predicting stock returns and volatility using consumption-aggregate wealth ratios: A nonlinear approach

Recent empirical evidence based on a linear framework tends to suggest that a Markov-switching version of the consumption-aggregate wealth ratio ( cay M S ), developed to account for structural breaks, is a better predictor of stock returns than the conventional measure ( cay )—a finding we confirm as well. Using quarterly data over 1952:Q1–2013:Q3, we however provide statistical evidence that the relationship between stock returns and cay or cay M S is in fact nonlinear. Then, given this evidence of nonlinearity, using a nonparametric Granger causality test, we show that it is in fact cay and not cay M S which is a stronger predictor of not only stock returns, but also volatility. • We examine the predictability of consumption-aggregate wealth ratios in stock markets. • Linear causality tests show that cay M S is a better predictor of returns. • We prove that the relationship between stock returns and cay or cay M S is nonlinear. • We show that cay ​and not cay M S is a stronger predictor of stock returns and volatility.

Public debt and growth in the euro area: evidence from parametric and nonparametric Granger causality

AbstractMany studies in the empirical literature show that public debt is negatively correlated with economic growth but there is no paper that studies the causal links between these variables using rigorous tests based on Granger’s ideas. Accordingly, we investigate the causal links between debt-to-GDP ratio and economic growth using both linear parametric and nonlinear nonparametric Granger causality tests. We focus on 12 euro countries for the period 1970–2012. Our empirical results suggest a unidirectional causality running from debt to economic growth for Spain and Portugal and a bidirectional causality for Belgium, Germany, Greece, Ireland and Italy. No causality in either direction is identified for Austria, Finland, Luxembourg and the Netherlands. Finally, for France, the tests provide evidence for a unidirectional causality running from GDP growth to debt-to-GDP ratio. In addition, the nonlinear tests indicate that overlooking nonlinearities may result in misleading conclusions about Granger causality. Caveats of the analysis, as well as policy conclusions, are also discussed.

Dynamic Relationship between CSI 300 Futures and Shanghai Composite Index: Analysis of Cointegration, Parametric and Nonparametric Granger Causality

Dynamic relationship between CSI 300 futures and Shanghai Composite Index will be explored in this paper based on five-minute high frequency data from 16th, April, 2010 to 31st, December, 2012. First of all, we found that index futures and its cash market exhibit a long-run equilibrium by applying Jonhenson Cointegration test, suggesting that at least one of the markets acts as price discovery for another. Subsequently, Vector Error Correction Model (VECM) should be conducted for the two markets that exhibit long-term equilibrium relationship and VECM model allows them to reflect the same information filtration. Furthermore, traditional (linear) Granger causality testing on raw data implies a bilateral causal relation between two markets. The linear interdependence of spot and futures can be further confirmed after excluding volatility spillover and time-varying conditional correlation effects from multivariate - Generalized Autoregressive Conditional Heteroskedasticity (Multivariate - GARCH). Finally, our non-parametric Granger causality results reveal that stock index futures plays a dominative rule in information delivery, even though there is a robust interrelation between futures and spot. Our results provide an insightful guideline for investors of China’s stock market and its index futures.

Granger causality revisited

This technical paper offers a critical re-evaluation of (spectral) Granger causality measures in the analysis of biological timeseries. Using realistic (neural mass) models of coupled neuronal dynamics, we evaluate the robustness of parametric and nonparametric Granger causality. Starting from a broad class of generative (state-space) models of neuronal dynamics, we show how their Volterra kernels prescribe the second-order statistics of their response to random fluctuations; characterised in terms of cross-spectral density, cross-covariance, autoregressive coefficients and directed transfer functions. These quantities in turn specify Granger causality — providing a direct (analytic) link between the parameters of a generative model and the expected Granger causality. We use this link to show that Granger causality measures based upon autoregressive models can become unreliable when the underlying dynamics is dominated by slow (unstable) modes — as quantified by the principal Lyapunov exponent. However, nonparametric measures based on causal spectral factors are robust to dynamical instability. We then demonstrate how both parametric and nonparametric spectral causality measures can become unreliable in the presence of measurement noise. Finally, we show that this problem can be finessed by deriving spectral causality measures from Volterra kernels, estimated using dynamic causal modelling.

Nonlinear Granger Causality: Guidelines for Multivariate Analysis

In this paper we propose an extension of the nonparametric Granger causality test, originally introduced by Diks and Panchenko [2006. A new statistic and practical guidelines for nonparametric Granger causality testing. Journal of Economic Dynamics & Control 30, 1647-1669]. We show that the basic test statistics lacks consistency in the multivariate setting. The problem is the result of the kernel density estimator bias, which does not converge to zero at a sufficiently fast rate when the number of conditioning variables is larger than one. In order to overcome this difficulty we apply the data-sharpening method for bias reduction. We then derive the asymptotic properties of the 'sharpened' test statistics and we investigate its performance numerically. We conclude with an empirical application to the US grain market.

Video Sensor-Based Complex Scene Analysis with Granger Causality

In this report, we propose a novel framework to explore the activity interactions and temporal dependencies between activities in complex video surveillance scenes. Under our framework, a low-level codebook is generated by an adaptive quantization with respect to the activeness criterion. The Hierarchical Dirichlet Processes (HDP) model is then applied to automatically cluster low-level features into atomic activities. Afterwards, the dynamic behaviors of the activities are represented as a multivariate point-process. The pair-wise relationships between activities are explicitly captured by the non-parametric Granger causality analysis, from which the activity interactions and temporal dependencies are discovered. Then, each video clip is labeled by one of the activity interactions. The results of the real-world traffic datasets show that the proposed method can achieve a high quality classification performance. Compared with traditional K-means clustering, a maximum improvement of 19.19% is achieved by using the proposed causal grouping method.

Dynamic changes in direction and frequency range of inter-areal cortical interactions revealed by non-parametric Granger causality

Models suggest that communication between brain areas could be mediated by oscillations in specific frequency bands. This hypothesis is supported by electrophysiological measurements wherein direction and frequency of interaction between brain areas varied during different stages of a cognitive task. Frequency-resolved granger causality (GC) is used often for this analysis, but it has been derived for stationary linear processes, which may not be appropriate for brain activity. Our goal was to determine whether for nonlinear processes conditional GC could still distinguish direct connections from indirect ones and to what extent dynamic changes in frequency & direction of interaction could be accurately detected. For this properties of GC determined parametrically, through fitting an autoregressive process of a fixed order, were compared to those obtained via non-parametric GC, which only uses measured spectral matrix. Oscillations in each cortical area were represented by a low-dimensional nonlinear model driven by white noise, whose standard deviation represented level of activity in respective areas. In addition, we analyzed responses from two coupled networks of spiking neurons in same way. We found that direction of interaction between reciprocally connected cortical areas was determined by level of activity, going from areas with high activity to those with low activity, which could be modulated on fast time scales. The frequency band of interaction was determined by sending area. For linear processes, parametric GC had lowest bias and variance compared to non-parametric GC, but was not appropriate for nonlinear model and network model, because oscillations could not be modeled accurately by autoregressive processes of a reasonable order. The non-parametric GC correctly represented ground truth connectivity when multi-taper spectral estimates were used, but when multi-tapering made spectral peaks too broad, artifacts emerged. Taken together, GC analysis revealed a simple rule for direction and frequency band of communication between cortical areas, specifically the loudest area gets heard, which can account for recent experimental results in which frequency band of communication was direction dependent.

Dynamic changes in direction and frequency range of inter-areal cortical interactions revealed by non-parametric Granger causality

Dynamic changes in direction and frequency range of inter-areal cortical interactions revealed by non-parametric Granger causality

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.

Financial variables and euro area growth: A non-parametric causality analysis

This paper investigates the predictive ability of financial variables for euro area growth through bivariate and multivariate non-parametric Granger causality tests. Apart from assessing the within-country forecasting ability of commonly-employed financial variables, such as the term spread, the stock market returns and the growth of real money supply, we also test for cross-country influences. In this way, we reveal the countries that are more useful in predicting growth in other member countries along with the ones that are more receptive to other countries' financial developments. Our results suggest that financial variables are useful leading indicators for euro area growth at a joint level, albeit at different horizons, ranging from one to six quarters. Our finding of overall increased levels of receptivity among member states provides useful information for policy makers, especially in the case of monetary union such as the euro area.

Analyzing multiple spike trains with nonparametric granger causality

Simultaneous recordings of spike trains from multiple single neurons are becoming commonplace. Understanding the interaction patterns among these spike trains remains a key research area. A question of interest is the evaluation of information flow between neurons through the analysis of whether one spike train exerts causal influence on another. For continuous-valued time series data, Granger causality has proven an effective method for this purpose. However, the basis for Granger causality estimation is autoregressive data modeling, which is not directly applicable to spike trains. Various filtering options distort the properties of spike trains as point processes. Here we propose a new nonparametric approach to estimate Granger causality directly from the Fourier transforms of spike train data. We validate the method on synthetic spike trains generated by model networks of neurons with known connectivity patterns and then apply it to neurons simultaneously recorded from the thalamus and the primary somatosensory cortex of a squirrel monkey undergoing tactile stimulation.

The nonlinear dynamic relationship of exchange rates: Parametric and nonparametric causality testing

The present study investigates the linear and nonlinear causal linkages among six currencies denoted relative to United States dollar (USD), namely Euro (EUR), Great Britain Pound (GBP), Japanese Yen (JPY), Swiss Frank (CHF), Australian Dollar (AUD) and Canadian Dollar (CAD). The data spans two periods between 3/20/1991 and 3/20/2007. We apply a new nonparametric test for Granger non-causality by Diks and Panchenko [Diks, C., Panchenko, V., 2005. A note on the Hiemstra–Jones test for Granger noncausality. Studies in Nonlinear Dynamics and Econometrics 9 (art. 4); Diks, C., Panchenko, V., 2006. A new statistic and practical guidelines for nonparametric Granger causality testing. Journal of Economic Dynamics & Control 30, 1647–1669] and the linear Granger test on the return time series. To detect strictly nonlinear causality, we examine the pairwise VAR-filtered residuals as well as in a six-variate formulation. We find remaining significant bi- and uni-directional causal nonlinear relationships in the series. Finally, we investigate causality after controlling for conditional heteroskedasticity using a GARCH–BEKK model. Whilst the nonparametric test statistics are smaller in some cases, significant nonlinear causal linkages persisted even after GARCH filtering during both periods. This indicates that currency returns may exhibit asymmetries and statistically significant higher-order moments.

Analyzing information flow in brain networks with nonparametric Granger causality

Multielectrode neurophysiological recording and high-resolution neuroimaging generate multivariate data that are the basis for understanding the patterns of neural interactions. How to extract directions of information flow in brain networks from these data remains a key challenge. Research over the last few years has identified Granger causality as a statistically principled technique to furnish this capability. The estimation of Granger causality currently requires autoregressive modeling of neural data. Here, we propose a nonparametric approach based on widely used Fourier and wavelet transforms to estimate both pairwise and conditional measures of Granger causality, eliminating the need of explicit autoregressive data modeling. We demonstrate the effectiveness of this approach by applying it to synthetic data generated by network models with known connectivity and to local field potentials recorded from monkeys performing a sensorimotor task.

Parametric and nonparametric Granger causality testing: Linkages between international stock markets

This study investigates long-term linear and nonlinear causal linkages among eleven stock markets, six industrialized markets and five emerging markets of South-East Asia. We cover the period 1987–2006, taking into account the on-set of the Asian financial crisis of 1997. We first apply a test for the presence of general nonlinearity in vector time series. Substantial differences exist between the pre- and post-crisis period in terms of the total number of significant nonlinear relationships. We then examine both periods, using a new nonparametric test for Granger noncausality and the conventional parametric Granger noncausality test. One major finding is that the Asian stock markets have become more internationally integrated after the Asian financial crisis. An exception is the Sri Lankan market with almost no significant long-term linear and nonlinear causal linkages with other markets. To ensure that any causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VAR filtered residuals and VAR filtered squared residuals for the post-crisis sample. We find quite a few remaining significant bi- and uni-directional causal nonlinear relationships in these series. Finally, after filtering the VAR-residuals with GARCH-BEKK models, we show that the nonparametric test statistics are substantially smaller in both magnitude and statistical significance than those before filtering. This indicates that nonlinear causality can, to a large extent, be explained by simple volatility effects.