Vector autoregression and causality: a theoretical overview and simulation study
综述了在水平向量自回归和误差修正模型中进行格兰杰因果关系检验的Wald检验理论，并基于模拟比较了三种序贯因果检验与常规检验的抽样性质。
This paper provides a theoretical overview of Wald tests for Granger causality in levels vector autoregressions (VAR's) and Johansen-type error correction models (ECM's). The theory is based on results in Toda and Phillips (1991a) and allows for stochastic and deterministic trends as well as arbitrary degrees of cointegration. We recommend some operational procedures for conducting Granger causality tests that are based on the Gaussian maximum likelihood estimation of ECM's. These procedures are applicable in the important practical case of testing the causal effects of one variable on another group of variables and vice versa. This paper also investigates the sampling properties of these testing procedures through simulation exercises. Three sequential causality tests in ECM's are compared with conventional causality tests in levels and differences VAR's.