VAR, Granger Causality and ARCH effects

[garchrookie]

Suppose I have the following VAR model with a lag of 3, then I can test the Granger-causality.

y_t = A + a1 y_t-1 + a2 y_t-2 + a3 y_t-3
b1 x_t-1 + b2 x_t-2 + b3 x_t-3 + e1t
x_t = B + c1 y_t-1 + c2 y_t-2 + c3 y_t-3
d1 x_t-1 + d2 x_t-2 + d3 x_t-3 + e2t

A joint F-test of the significance of (b1,b2,b3) shows whether x granger-causes y with the first equation.

A joint F-test of the significance of (c1,c2,c3) shows whether y granger-causes x with the second equation.

However, if the x_t and y_t have significant ARCH effects. Then, the F-statistics is not hetero robust?

What can we do for this case? Is there any sample WinRATS program that provide a joint test statistics that is hetero-robust?

[TomDoan]

With the two variable system, you can do:

Code: Select all

LINREG(ROBUST) Y
# CONSTANT Y{1 2 3} X{1 2 3}
EXCLUDE
# X{1 2 3}

and similarly for Y causing X. Now that doesn't correct for GARCH effects, since it will only handle heteroscedasticity conditional on the regressors (lags of Y and X). If you're sure that you have GARCH effects, the simplest thing to do is to just estimate the MV-GARCH model, and do the tests afterwards using the TEST instruction.