cointegrating

The parameters of an estimated cointegrating relation are called the cointegrating vector.

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In multivariate models there may be more than one such cointegrating vector.

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The first cointegrating relation has no significant effect on the capital equation.

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The Johansen methodology is used to test for the number of cointegrating vectors in the multivariate Vector Error Correction Model (VECM) estimate their parameters, and the rate at which energy use and economic activity adjusts to disequilibrium in the long-run relations.

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If a multivariate approach helps uncover the direction of Granger causality between energy and GDP, then a multivariate approach should clarify the cointegrating relations among variables.

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The cointegrating vectors indicate that energy use and GDP are present in both cointegrating relations but the elements of α indicate that these cointegrating relations affect the equation for energy use only.

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The test for the number of cointegrating vectors determines the dimensions of α and β.

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We have multiple time series and we have an unknown number of cointegrating relationships.

More on MBH98 Figure 7 « Climate Audit 2006

The Exit Route Theory of Globalisation and the Efficacy of Monetary Policy. cointegrating vectors (r = 3).

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The VECM is given by: in which y is a vector of variables (in logarithms), ε t is a vector of random disturbances, Δ is the first difference operator, t is a deterministic time trend, y is a vector of coefficients to be estimated, α is a matrix of adjustment coefficients (to be estimated), β is the matrix of cointegrating vectors (to be estimated), and the Γi are matrices of short-run dynamics coefficients (to be estimated).

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