Non-Asymptotic Guarantees for Robust Identification of Granger Causality via the LASSO

Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data durations to be useful and are not immune to confounding effects. In this work, we close this gap by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish that the sufficient conditions of LASSO also suffice for robust identification of Granger causal influences. We also characterize the false positive error probability of a simple thresholding rule for identifying Granger causal effects. We present simulation studies and application to real data to compare the performance of the ordinary least squares and LASSO in detecting Granger causal influences, which corroborate our theoretical results

Robust inference of causality in high-dimensional dynamical processes from the Information Imbalance of distance ranks

We introduce an approach which allows inferring causal relationships between variables for which the time evolution is available. Our method builds on the ideas of Granger Causality and Transfer Entropy, but overcomes most of their limitations. Specifically, our approach tests whether the predictability of a putative driven system Y can be improved by incorporating information from a potential driver system X, without making assumptions on the underlying dynamics and without the need to compute probability densities of the dynamic variables. Causality is assessed by a rigorous variational scheme based on the Information Imbalance of distance ranks, a recently developed statistical test capable of inferring the relative information content of different distance measures. This framework makes causality detection possible even for high-dimensional systems where only few of the variables are known or measured. Benchmark tests on coupled dynamical systems demonstrate that our approach outperforms other model-free causality detection methods, successfully handling both unidirectional and bidirectional couplings, and it is capable of detecting the arrow of time when present. We also show that the method can be used to robustly detect causality in electroencephalography data in humans.Comment: Extended acknowledgments Sectio

Simulation Evidence on Granger Causality in Presence of a Confounding Variable

This paper provides simulation evidence on Granger causality between two variables when they are jointly caused by a third variable. Four Data Generating Processes (DGPs) are considered for testing causality by Granger method and two DGPs for testing causality by Toda and Yamamoto (1995) procedure. Our simulation involve three variables but causality has been tested only between two variable and the third variable (the real cause) has been ignored to show that its association which matters in these causality tests. Nevertheless, if we know that there are only two variables in economic dynamics and the true model is known then these causality tests work fine and for this we have carried out bootstrap simulation.Granger Causality, Toda and Yamamoto Procedure, Monte Carlo Simulation, Causation and Association, Bootstrap Simulation

Does Government Expenditure on Education Promote Economic Growth? An Econometric Analysis

Education being an important component of human capital has always attracted the interests of economists, researchers and policy makers. Governments across the globe in general and in India in particular are trying to improve the human capital by pumping more investments in education. But the issue that whether improved level of education resulting from more education spending can promote economic growth is still controversial. Some economists and researchers have supported the bi-directional relation between these two variables, while it has also been suggested that it is the economic growth that stimulates governments spend more on education, not the other way. Considering this research issue, the present paper uses linear and non-linear Granger Causality methods to determine the causal relationship between education spending and economic growth in India for the period 1951-2009. The findings of this paper indicate that economic growth affects the level of government spending on education irrespective of any lag effects, but investments in education also tend to influence economic growth after some time-lag. The results are particularly useful in theoretical and empirical research by economists, regulators and policy makers

Detecting and tracking time-varying causality with applications to EEG data

This paper introduces a novel method called the ERR-Causality, or Error Reduction Ratio Causality test, that can be used to detect and track causal relationships between two signals using a new adaptive forward orthogonal least squares (Adaptive-Forward-OLS) algorithm. In comparison to the traditional Granger method, one advantage of the new ERR-Causality test is that it can effectively detect the time-varying direction of linear or nonlinear causality between two signals without fitting a complete model. Another important advantage is that the ERR-Causality test can detect both the direction of interactions and estimate the relative time shift between the two signals. Several numerical examples are provided to illustrate the effectiveness of the new method for causal relationship detection between two signals. An important real application, relating to the analysis of the causality of EEG signals from different cortical sites which can be very useful for understanding brain activity during an epileptic seizure by inspecting the high-resolution time varying directed information flow, is also discussed

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

Towards a sharp estimation of transfer entropy for identifying causality in financial time series

We present an improvement of an estimator of causality in financial time series via transfer entropy, which includes the side information that may affect the cause-effect relation in the system, i.e. a conditional information-transfer based causality. We show that for weakly stationary time series the conditional transfer entropy measure is nonnegative and bounded below by the Geweke's measure of Granger causality. We use k-nearest neighbor distances to estimate entropy and approximate the distribution of the estimator with bootstrap techniques. We give examples of the application of the estimator in detecting causal effects in a simulated autoregressive stationary system in three random variables with linear and non-linear couplings; in a system of non stationary variables; and with real financial data.Postprint (published version

Estimating the Effects of Interest Rates on Share Prices Using Multi-scale Causality Test in Emerging Markets: Evidence from Turkey

This paper examines the impacts of changes in interest rates on stock returns by using wavelet analysis with Granger causality test. Financial time series in non-coherent markets should be analyzed by advanced methods capturing complexity of the markets and non-linearities in stock returns. As a semi-parametric method, wavelets analysis might be superior to detect the chaotic patterns in the non-coherent markets. By using daily closing values of the ISE 100 Index and compounded interest rates, it is proven that and starting with 9 days time-scale effect interest rate is granger cause of ISE 100 index and the effects of interest rates on stock return increases with higher time-scales. This evidence shows that bond market has significant long-term effect on stock market for Turkey and traders should consider long-term money markets changes as well as short-term changes.Interest rates; Emerging markets; Wavelets; Stock returns; Multi-scale Granger causality