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The Granger causality test The Granger causality test for the case of two stationary variables y_(t) and x_(t) involves as a first step the estimation of the following VAR model: y_(t)=a_(1)+\sum_(i=1)^n \beta _(i)x_(t-i)+\sum_(j=1)^m \gamma _(j)y_(t-j)+e_(1t) x_(t)=a_(2)+\sum_(i=1)^n \theta _(i)x_(t-i)+\sum_(j=1)^m \delta _(j)y_(t-j)+e_(2t) Vector Autoregressive (VAR) Models and Causality Tests 323 where it is assumed that both \epsi _(yt) and \epsi _(xt) are uncorrelated white-noise error terms. In this model we can have the following different cases: Case 1 The lagged x terms in Equation (15.10) may be statistically different from zero as a group, and the lagged y terms in Equation (15.11) not statistically different from zero. In this case we see x_(t) causes y_(t). Case 2 The lagged y terms in Equation (15.11) may be statistically different from zero as a group, and the lagged x terms in Equation (15.10) not statistically different from zero. In this case we see that y_(t) causes x_(t). Case 3 Both sets of x and y terms are statistically different from zero in Equations (15.10) and (15.11), so that there is bi-directional causality. Case 4 Both sets of x and y terms are not statistically different from zero in Equations (15.10) and (15.11), so that x_(t) is independent of y_(t).

Name: the granger causality test the granger causality test for the case of two stationary variables yt and xt involves as a first step the estimation of the following var model yta1sumi1n be 63089
Uploaded: 2021-06-04T16:15:31-08:00
Duration: 8 min 28 s
Channel: Heather Duong
Description: the granger causality test the granger causality test for the case of two stationary variables yt and xt involves as a first step the estimation of the following var model yta1sumi1n be 63089

          The Granger causality test
The Granger causality test for the case of two stationary variables y_(t) and x_(t) involves as a first step the estimation of the following VAR model:
y_(t)=a_(1)+\sum_(i=1)^n \beta _(i)x_(t-i)+\sum_(j=1)^m \gamma _(j)y_(t-j)+e_(1t)
x_(t)=a_(2)+\sum_(i=1)^n \theta _(i)x_(t-i)+\sum_(j=1)^m \delta _(j)y_(t-j)+e_(2t)
Vector Autoregressive (VAR) Models and Causality Tests
323
where it is assumed that both \epsi _(yt) and \epsi _(xt) are uncorrelated white-noise error terms. In this model we can have the following different cases:
Case 1 The lagged x terms in Equation (15.10) may be statistically different from zero as a group, and the lagged y terms in Equation (15.11) not statistically different from zero. In this case we see x_(t) causes y_(t).
Case 2 The lagged y terms in Equation (15.11) may be statistically different from zero as a group, and the lagged x terms in Equation (15.10) not statistically different from zero. In this case we see that y_(t) causes x_(t).
Case 3 Both sets of x and y terms are statistically different from zero in Equations (15.10) and (15.11), so that there is bi-directional causality.
Case 4 Both sets of x and y terms are not statistically different from zero in Equations (15.10) and (15.11), so that x_(t) is independent of y_(t).

Added by Andr-S P.

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