## Wednesday, April 18, 2012

### Surplus-Lag Granger Causality Testing

My previous posts (here, here, and especially here) on Granger causality testing have attracted more interest than I anticipated. One of the things that I've discussed at some length is the "surplus-lag" approach that can be used when the data are possibly non-stationary and possibly cointegrated. In particular I've talked about the Toda and Yamamoto (1995) procedure, but there are alternatives such as those introduced by Dolado anLütkepohl  (1996) and Saikkonen and Lütkepohl (1996).

These modifications to the standard approach to testing for Granger (non-) causality are needed to ensure that the Wald test statistic has its usual chi-square asymptotic null distribution. You can't just test in the usual way unless the data are stationary. In fact, the "surplus lag" approach has advantages even beyond those that we knew about already.