Keywords: Conditional Granger-causality, Multivariate time series, Quantile regression, Specification test
Granger causality analysis is a popular method for inference on directed interactions in economics of many variables. A shortcoming of the standard linear regression framework for Granger causality is that it only identifies the pair causal pattern. However, interactions do not necessarily take place between pair variables, but may be mediated by the other variables. Building on Geweke's (1984) and Troster's (2016) seminal work, we offer additional justifications for one particular form of multivariate Granger causality based on the parametric dynamic quantile regressive models in this study that evaluate nonlinear causality and possible causal relations in all conditional quantiles. We present Monte Carlo experiments and an application considering the causal relations between stock market trading volume, returns and exchange rates for both domestic and cross-country markets by using the daily data of the three financial markets: China, Japan, Korea. We find the causal effects of stock returns and trading volume cause exchange rate are heterogeneous across quantiles. In contrast with Granger causality in mean and Granger causality in quantile, our results support a comprehensive and theoretically consistent extension of Granger causality to identify actual causal patterns in the multivariate case.