Granger test is used to check cause-effect relations of time series.
To calculate the test, the series must be of equal length (have equal number of points). The series length must satisfy the following relation:
L ≥ 3 *m + 3
Where:
L. The number of series points.
m. Lag.
The idea behind the Granger test is as follows: if the variable x affects the variable y, changes in x must precede the changes in y, but not the other way round. Thus, there are two conditions which must be satisfied:
x must contribute to the forecast of y.
y must not significantly contribute to the forecast of x.
If both variables are significantly useful in forecasting each other, probably there exists a third variable z, which affects both x and y. To test the null hypothesis that x does not affect y, we should estimate the regression of y on lagged y values and lagged x values:
For this model, the hypothesis that x does no affect y is defined similarly to testing of the hypothesis of redundant variables:
The hypothesis is checked based on F-test.
The hypothesis that y does no affect x is tested in the same way, just swap x and y in the regression equation.
To decide that x affects y, it is required to reject the hypothesis that x does not affect y, and accept the hypothesis y does not affect x.
Remember that "x affects y" does not mean that there is cause-effect relation between these variables; this rather means that the previous values of x explain the subsequent values of y, that means a possibility of cause-effect relations. If the hypothesis "x does not affect y" is not rejected, this means that x is not the cause of y.
It is recommended to repeat this test for several values of m to discover to what extent the choice of m affects the test results.
See also:
Library of Methods and Models | IMsGrangerTestSettings