A Research Of Linear And Non-linear Causality System

Granger causality(GC)has been widely applied to various fields so far.In 2011,Hu et al.proposed new causality(NC)method and revealed true causality in time-invariant bivariate autoregressive model compared with GC.In this thesis,we firstly studied the causality system and provided evidence of the limitation of GC,and exhibited the difference between GC and NC in a mathematical way.We find that there exists a fatal drawback in Granger causality.By deriving the mathematical formula of the regression model in case of the order m=1 or 2,we found the Granger causality might lose the information of some coefficients,which means GC value cannot represent the true causality necessarily.By several illustrative examples we found that the new causality can be more accurate than the Granger causality.Moreover,we considered a recently proposed convergent cross-mapping(CCM)method which is used to analyze causality relationship of nonlinear dynamical system.We pointed out its drawback by the fact that in the method one may use the future value to predict the future value.Compared with CCM,we proved that the NC method can reflect evident causality relationship between variables.We then extend NC method from linear model to nonlinear model in time domain based on the above analyses.We proposed a causality method of nonlinear model of two time series called proportional-based causality(PBC)in which the core idea is to use the proportion concept.Several illustrative examples showed the feasibility of PBC method and the advantages against CCM method.PBC will be widely applied in many fields.