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.

[xiaoxi]

Dear Tom,

I would like to test the Granger Causality among inflation, output growth and nominal and real uncertainty. Is that true that I cannot do the causality test based on BEKK model since the BEKK model restricts the effects of uncertainties to being positive? What if I run the causality test based on Asymmetric BEKK? (See Stilianos Fountas et al. (2006) ''Inflation Unvertainty, Output Growth Uncertainty and Macroeconomic Performance'') Do I have to change to CCC GARCH model or are there other ways to address this problem?

I hope that I made my statement clearly.

Thanks very much for your help.

Xiaoxi

[TomDoan]

Dear Tom,

I would like to test the Granger Causality among inflation, output growth and nominal and real uncertainty. Is that true that I cannot do the causality test based on BEKK model since the BEKK model restricts the effects of uncertainties to being positive? What if I run the causality test based on Asymmetric BEKK? (See Stilianos Fountas et al. (2006) ''Inflation Unvertainty, Output Growth Uncertainty and Macroeconomic Performance'') Do I have to change to CCC GARCH model or are there other ways to address this problem?

I hope that I made my statement clearly.

Thanks very much for your help.

Xiaoxi

I have no idea what their point is. A CC GARCH with positive coefficients on the lagged squared residuals (and if they're not positive you have real problems) does more to "restrict" the effects of uncertainties to be positive than a BEKK does. And they're testing GC in the mean anyway, so there is no real direct connection between the method used for estimating the uncertainty and its effect on the mean. It's possible that it's difficult to fit a BEKK model to all of those countries. BEKK in general is harder to fit than a CC model, particularly when the size of the parameter space gets large with all those lag parameters, so they may have decided to go with the simpler model because it would work for each country. But the rationale for it is suspect.