Granger causality test with trend stationay variable

[JosePerles]

Hello, can anyone help me with this issue?

I want to make a Granger causality analysis with two variables. One of them "market share" is "trend stationary" (linear and quadratic) and the other one "GDP" is non-stationary (integrated of order 1). The Granger causality test is for stationary variables, then...which of the following would be most appropriate?

1).-Differentiating the non-stationary variable "GDP" and apply directly the Granger test by using the Causality test option in "group statistics".

2).-Differentiating the non stationary variable "GDP", estimating a VAR with trend (due that the other variable is trend stationary, and I have found that the variables are not cointegrated) and apply the Granger test after VAR estimation to account for this linear and quadratic trend.

or

3).-Differentiate both variables and apply the Granger test directly by using the test in "group statistics".


I wonder which approach is more appropriate. Thanks in advance and sorry for any inconvenience.

José F. Perles

[Basyvava]

Good question. First, I think there's no point in differentiating the stationary variable for the Granger test, it should be fine as it is. Second, running a Granger on both stationary variables (one is I(0) and the other I(1)) should give the same results whether or not you estimate a VAR before.