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 limultaneously recorded from the thalamus and the primary somatosensory cortex of a squirrel monkey undergoing tactile stimulation.

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.

Is Granger Causality a Viable Technique for Analyzing fMRI Data?

Multivariate neural data provide the basis for assessing interactions in brain networks. Among myriad connectivity measures, Granger causality (GC) has proven to be statistically intuitive, easy to implement, and generate meaningful results. Although its application to functional MRI (fMRI) data is increasing, several factors have been identified that appear to hinder its neural interpretability: (a) latency differences in hemodynamic response function (HRF) across different brain regions, (b) low-sampling rates, and (c) noise. Recognizing that in basic and clinical neuroscience, it is often the change of a dependent variable (e.g., GC) between experimental conditions and between normal and pathology that is of interest, we address the question of whether there exist systematic relationships between GC at the fMRI level and that at the neural level. Simulated neural signals were convolved with a canonical HRF, down-sampled, and noise-added to generate simulated fMRI data. As the coupling parameters in the model were varied, fMRI GC and neural GC were calculated, and their relationship examined. Three main results were found: (1) GC following HRF convolution is a monotonically increasing function of neural GC; (2) this monotonicity can be reliably detected as a positive correlation when realistic fMRI temporal resolution and noise level were used; and (3) although the detectability of monotonicity declined due to the presence of HRF latency differences, substantial recovery of detectability occurred after correcting for latency differences. These results suggest that Granger causality is a viable technique for analyzing fMRI data when the questions are appropriately formulated.

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.

Effect of measurement noise on Granger causality

Most of the signals recorded in experiments are inevitably contaminated by measurement noise. Hence, it is important to understand the effect of such noise on estimating causal relations between such signals. A primary tool for estimating causality is Granger causality. Granger causality can be computed by modeling the signal using a bivariate autoregressive (AR) process. In this paper, we greatly extend the previous analysis of the effect of noise by considering a bivariate AR process of general order p. From this analysis, we analytically obtain the dependence of Granger causality on various noise-dependent system parameters. In particular, we show that measurement noise can lead to spurious Granger causality and can suppress true Granger causality. These results are verified numerically. Finally, we show how true causality can be recovered numerically using the Kalman expectation maximization algorithm.

Granger causality of coupled climate processes: Ocean feedback on the North Atlantic oscillation

This study uses a Granger causality time series modeling approach to quantitatively diagnose the feedback of daily sea surface temperatures (SSTs) on daily values of the North Atlantic Oscillation (NAO) as simulated by a realistic coupled general circulation model (GCM). Bivariate vector autoregressive time series models are carefully fitted to daily wintertime SST and NAO time series produced by a 50-yr simulation of the Third Hadley Centre Coupled Ocean-Atmosphere GCM (HadCM3). The approach demonstrates that there is a small yet statistically significant feedback of SSTs oil the NAO. The SST tripole index is found to provide additional predictive information for the NAO than that available by using only past values of NAO-the SST tripole is Granger causal for the NAO. Careful examination of local SSTs reveals that much of this effect is due to the effect of SSTs in the region of the Gulf Steam, especially south of Cape Hatteras. The effect of SSTs on NAO is responsible for the slower-than-exponential decay in lag-autocorrelations of NAO notable at lags longer than 10 days. The persistence induced in daily NAO by SSTs causes long-term means of NAO to have more variance than expected from averaging NAO noise if there is no feedback of the ocean on the atmosphere. There are greater long-term trends in NAO than can be expected from aggregating just short-term atmospheric noise, and NAO is potentially predictable provided that future SSTs are known. For example, there is about 10%-30% more variance in seasonal wintertime means of NAO and almost 70% more variance in annual means of NAO due to SST effects than one would expect if NAO were a purely atmospheric process.

A fast and robust statistical test based on likelihood ratio with Bartlett correction to identify Granger causality between gene sets

We propose a likelihood ratio test ( LRT) with Bartlett correction in order to identify Granger causality between sets of time series gene expression data. The performance of the proposed test is compared to a previously published bootstrapbased approach. LRT is shown to be significantly faster and statistically powerful even within non- Normal distributions. An R package named gGranger containing an implementation for both Granger causality identification tests is also provided.

Granger causality among house price and macroeconomic variables in Victoria

This study analyses the dynamic causality of four macroeconomic variables on house prices. The four macroeconomic variables have interrelationships with house prices in certain lagged terms, but these relationships are not always the same as the notions put forward in prior research. The relationships are detected to be unstable in the three observation periods. The instability of these relationships would cause difficulty in predicting house prices in the market, especially for policy makers and market participants.

Female labour force participation, fertility and infant mortality in Australia : some empirical evidence from Granger causality tests

This study applies Granger causality tests within a multivariate error correction framework to examine the relationship between female participation rates, infant mortality rates and fertility rates for Australia using annual data from 1960 to 2000. Decomposition of variance and impulse response functions are also considered. The main findings are twofold. First, in the short run there is unidirectional Granger causality running from the fertility rate to female labour force participation and from the infant mortality rate to female labour force participation while there is neutrality between the fertility rate and infant mortality rate. Second, in the long run both the fertility rate and infant mortality rate Granger cause female labour participation.

Higher education, real income and real investment in China : evidence from Granger causality tests

This paper employs cointegration and error-correction modelling to test the causal relationship between real income, real investment and tertiary education using data for the People's Republic of China over the period 1952-1999. To proxy tertiary education we use higher education enrolments and higher education graduates in alternative empirical specifications. One of the paper's main findings is that real income, real investment and tertiary education are cointegrated when real investment is the dependent variable, but are not cointegrated when either tertiary education or real income is the dependent variable. We also extend the in-sample analysis to examine the decomposition of variance and impulse response functions.

Multivariate granger causality between electricity consumption, exports and GDP : Evidence from a panel of Middle Eastern countries

This paper examines the causal relationship between electricity consumption, exports and gross domestic product (GDP) for a panel of Middle Eastern countries. We find that for the panel as a whole there are statistically significant feedback effects between these variables. A 1 per cent increase in electricity consumption increases GDP by 0.04 per cent, a 1 per cent increase in exports increases GDP by 0.17 per cent and a 1 per cent increase in GDP generates a 0.95 per cent increase in electricity consumption. The policy implications are that for the panel as a whole these countries should invest in electricity infrastructure and step up electricity conservation policies to avoid a reduction in electricity consumption adversely affecting economic growth. Further policy implications are that for the panel as a whole promoting exports, particularly non-oil exports, is a means to promote economic growth and that expansion of exports can be realized without having adverse effects on energy conservation policies.

New Zealand’s trade balance : evidence of the J-curve and granger causality

This article tests for the existence of any cointegration relationship between trade balance and real effective exchange rate (REER), foreign income and domestic income for New Zealand during the period 1970-2000. It also examines the direction of the casual relationship between the above variables, and applies the impulse response analysis to determine whether shocks to the REER induce the trade balance to follow a J-curve pattern. The results indicate that there is no cointegration relationship between the above variables; there is a casual connection in both directions between trade balance and foreign income; and New Zealand's trade balance exhibits a J-curve pattern when there is a depreciation of the New Zealand dollar.