It is well known that in a vector autoregressive (VAR) model Granger non-causality is characterized by a set of restrictions on the VAR coefficients. This characterization has been derived under the assumption of non-singularity of the covariance matrix of the innovations. This note shows that if this assumption is violated, then the characterization of Granger non-causality in a VAR model fail...

Causal inference among high-dimensional time series data proves an important research problem in many fields. While in the classical regime one often establishes causality among time series via a concept known as “Granger causality,” existing approaches for Granger causal inference in high-dimensional data lack the means to characterize the uncertainty associated with Granger causality estimate...

Attempts to identify causal interactions in multivariable biological time series (e.g., gene data, protein data, physiological data) can be undermined by the confounding influence of environmental (exogenous) inputs. Compounding this problem, we are commonly only able to record a subset of all related variables in a system. These recorded variables are likely to be influenced by unrecorded (lat...

This paper examines the causality between concentration in banking industry and economic growth by using data across 15 countries named in "Iran outlook in 2025", over the period 2004-2011. Our aim is to assess whether the economy grows more or less rapidly in areas where the banking sector is more concentrated. The topic is motivated by the fact that the causality between concentration in bank...

Granger causality has been applied to explore predictive causal relations among multiple time series in various fields. However, the existence of non-stationary distributional changes among the time series variables poses significant challenges. By analysing a real dataset, we observe that factors such as noise, distribution changes and shifts increase the complexity of the modelling, and large...

Forecasters and applied econometricians are often interested in comparing the predictive accuracy of nested competing models. A leading example of nestedness is when predictive ability is equated with “out-of-sample Granger causality”. In particular, it is often of interest to assess whether historical data from one variable are useful when constructing a forecasting model for another variable,...

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....

Using data from a repeated public good game, I conduct a Granger causality test and find that contributions and beliefs about the contributions of others decline together, with neither variable leading the other. As a result, I model contributions and beliefs using a system of simultaneous equations. Estimating the system provides evidence on the magnitude of the projection bias. Since contribu...

This paper describes the implied volatility function computed from options on the Italian stock market index between 1995 and 1998 and tries to find out potential explanatory variables. We find that the typical smirk observed for S&P500 stock index characterizes also Mib30 stock index. When potential determinants are investigated by a linear Granger Causality test, the important role played by ...

This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. This paper forecasts inflation in Sudan following two methodo...