Chuck A Arize
Identify and Prepare Data:Ensure your time series data is non-stationary and integrated of the same order, typically I(1). Test for Cointegration:Use Johansen's cointegration test to determine if there is a long-run equilibrium relationship between the variables. Estimate the VECM:Specify and estimate the VECM based on the results of the cointegration test. The VECM includes both the short-term dynamics and the long-term equilibrium relationship. Specify the VECM: The VECM can be written as: Δyt=Πyt−1+∑i=1k−1ΓiΔyt−i+ϵt\Delta y_t = \Pi y_{t-1} + \sum_{i=1}^{k-1} \Gamma_i \Delta y_{t-i} + \epsilon_tΔyt=Πyt−1+i=1∑k−1ΓiΔyt−i+ϵtwhere Π=αβ′\Pi = \alpha \beta'Π=αβ′, Δyt\Delta y_tΔyt is the vector of differenced variables, α\alphaα represents the speed of adjustment to the long-term equilibrium, and β′\beta'β′ contains the cointegration vectors. Perform Granger Causality Tests:Test for Granger causality by examining the significance of the lagged differenced terms and the error correction term in the VECM. Typically, you will test the null hypothesis that the coefficients of the lagged differenced terms of one variable are equal to zero in the equation of another variable. Interpret Results:If the coefficients of the lagged differenced terms are statistically significant, you can reject the null hypothesis, indicating Granger causality. Additionally, the significance of the error correction term (α\alphaα) provides information about the long-term causality.
To construct and test for Granger causality in a Vector Error Correction Model (VECM), follow these steps:
In practice, software like EViews, R, or Stata can be used to estimate VECM and perform Granger causality tests.
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Chuck A Arize
To test for Granger causality in a Vector Error Correction Model (VECM), first establish the cointegration relationships among the variables using the VECM framework. Then, perform Granger causality tests on the variables by examining the lagged values of the variables within the VECM to determine if past values of one variable help predict future values of another.
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