Supervised estimation of Granger-based causality between time series

Brain effective connectivity aims to detect causal interactions between distinct brain units and it is typically studied through the analysis of direct measurements of the neural activity, e.g., magneto/electroencephalography (M/EEG) signals. The literature on methods for causal inference is vast. It includes model-based methods in which a generative model of the data is assumed and model-free methods that directly infer causality from the probability distribution of the underlying stochastic process. Here, we firstly focus on the model-based methods developed from the Granger criterion of causality, which assumes the autoregressive model of the data. Secondly, we introduce a new perspective, that looks at the problem in a way that is typical of the machine learning literature. Then, we formulate the problem of causality detection as a supervised learning task, by proposing a classification-based approach. A classifier is trained to identify causal interactions between time series for the chosen model and by means of a proposed feature space. In this paper, we are interested in comparing this classification-based approach with the standard Geweke measure of causality in the time domain, through simulation study. Thus, we customized our approach to the case of a MAR model and designed a feature space which contains causality measures based on the idea of precedence and predictability in time. Two variations of the supervised method are proposed and compared to a standard Granger causal analysis method. The results of the simulations show that the supervised method outperforms the standard approach, in particular it is more robust to noise. As evidence of the efficacy of the proposed method, we report the details of our submission to the causality detection competition of Biomag2014, where the proposed method reached the 2nd place. Moreover, as empirical application, we applied the supervised approach on a dataset of neural recordings of rats obtaining an important reduction in the false positive rate

Classification-based prediction of effective connectivity between timeseries with a realistic cortical network model

Effective connectivity measures the pattern of causal interactions between brain regions. Traditionally, these patterns of causality are inferred from brain recordings using either non-parametric, i.e., model-free, or parametric, i.e., model-based, approaches. The latter approaches, when based on biophysically plausible models, have the advantage that they may facilitate the interpretation of causality in terms of underlying neural mechanisms. Recent biophysically plausible neural network models of recurrent microcircuits have shown the ability to reproduce well the characteristics of real neural activity and can be applied to model interacting cortical circuits. Unfortunately, however, it is challenging to invert these models in order to estimate effective connectivity from observed data. Here, we propose to use a classification-based method to approximate the result of such complex model inversion. The classifier predicts the pattern of causal interactions given a multivariate timeseries as input. The classifier is trained on a large number of pairs of multivariate timeseries and the respective pattern of causal interactions, which are generated by simulation from the neural network model. In simulated experiments, we show that the proposed method is much more accurate in detecting the causal structure of timeseries than current best practice methods. Additionally, we present further results to characterize the validity of the neural network model and the ability of the classifier to adapt to the generative model of the data

Non-Parametric Causality Detection: An Application to Social Media and Financial Data

According to behavioral finance, stock market returns are influenced by emotional, social and psychological factors. Several recent works support this theory by providing evidence of correlation between stock market prices and collective sentiment indexes measured using social media data. However, a pure correlation analysis is not sufficient to prove that stock market returns are influenced by such emotional factors since both stock market prices and collective sentiment may be driven by a third unmeasured factor. Controlling for factors that could influence the study by applying multivariate regression models is challenging given the complexity of stock market data. False assumptions about the linearity or non-linearity of the model and inaccuracies on model specification may result in misleading conclusions. In this work, we propose a novel framework for causal inference that does not require any assumption about the statistical relationships among the variables of the study and can effectively control a large number of factors. We apply our method in order to estimate the causal impact that information posted in social media may have on stock market returns of four big companies. Our results indicate that social media data not only correlate with stock market returns but also influence them.Comment: Physica A: Statistical Mechanics and its Applications 201

A non-linear Granger-causality framework to investigate climate-vegetation dynamics

Satellite Earth observation has led to the creation of global climate data records of many important environmental and climatic variables. These come in the form of multivariate time series with different spatial and temporal resolutions. Data of this kind provide new means to further unravel the influence of climate on vegetation dynamics. However, as advocated in this article, commonly used statistical methods are often too simplistic to represent complex climate-vegetation relationships due to linearity assumptions. Therefore, as an extension of linear Granger-causality analysis, we present a novel non-linear framework consisting of several components, such as data collection from various databases, time series decomposition techniques, feature construction methods, and predictive modelling by means of random forests. Experimental results on global data sets indicate that, with this framework, it is possible to detect non-linear patterns that are much less visible with traditional Granger-causality methods. In addition, we discuss extensive experimental results that highlight the importance of considering non-linear aspects of climate-vegetation dynamics

Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions

Hawkes (1971) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this paper it is shown that the Granger causality structure of such processes is fully encoded in the corresponding link functions of the model. A new nonparametric estimator of the link functions based on a time-discretized version of the point process is introduced by using an infinite order autoregression. Consistency of the new estimator is derived. The estimator is applied to simulated data and to neural spike train data from the spinal dorsal horn of a rat.Comment: 20 pages, 4 figure

On The Predictive Content Of Production Surveys: A Pan-European Study

For over forty years, Business Tendency Surveys have been collected in multiple member states of the European Union. Previous research has studied the predictive accuracy of the expectation variables included in those surveys through bivariate, within-country, Granger-causality tests, which has resulted in mixed conclusions. We extend previous research in various ways, as we (i) explicitly allow for cross-country influences, and (ii) do so using both bivariate and multivariate Granger-causality tests. Specifically, the multivariate El-Himdi and Roy test is adapted to jointly test the forecasting value of multiple production expectation series, to assess whether part of this joint effect is indeed due to cross-country influences, and to determine which countries' expectation series have most "clout" in predicting the production levels in the other member countries, or have higher "receptivity", in that their production levels are Granger-caused by the other countries' expectations.business surveys;cross-correlations;granger causality;production expectations