If data are I (1) but not cointegrated, Granger Causality test requires transformation of the data to make them I (0). So if I don't transform them, is it true that causality Granger doesn't exist?
In general, if all the series are stationary (I(0)), we estimate a VAR model using the levels of the data and we can apply the Granger causality tests. If the series are I(1) but not cointegrated we estimate a VAR model using the first differences of the data and we can apply the Granger causality tests. When the series are cointegrated, we estimate a VEC model and we can apply the Granger causality tests.
The Granger causality test can be applied for stationary series as a test for whether a variable is exogenous or endogenous in a VAR system. If no variables in a model affect a particular variable it can be viewed as exogenous.
Yes, You have to transform it to make it 1(0) , as the variables are not cointegrated, otherwise you will be estimating spurious trends and not the underlying causality of the variables . If cointegrated by first differencing one , also throws underlying causes by removing trends ., and therefore VECM is being done .
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