Causality in Nonlinear

The concepts of weak, strong and strict Granger causality are introduced for nonlinear time series models. 1-step ahead predictions are formed using the conditional expectation. The weak form is related to Granger's original deenition for linear predictors in that it is based on the forecast error variance, whereas the strong form concerns the conditional variance, and the strict form the conditional distribution. Necessary and suucient conditions for noncausality are derived for a regime switching VAR with residuals that are Gaussian conditional on the regime. In such models, the strong and strict forms are equivalent and imply linear restrictions, while the weak form produces nonlinear constraints. As an illustration, the hypotheses are tested using monthly U.S. data on money and income.