nomadbrown.blogg.se - Granger causality testing

GRANGER CAUSALITY TESTING SERIAL
GRANGER CAUSALITY TESTING SERIES

If all of the time-series are stationary, m = 0, and you would (correctly) just test for non-causality in the 'old-fashioned' way: estimate a levels VAR and apply the Wald test to the relevant coefficients.

If you fail to use the T-Y approach (adding, but not testing, the 'extra' m lags), or some equivalent procedure, and just use the usual Wald test, your causality test results will be meaningless, even asymptotically.

normal if the data are non-stationary, and there are also pre-testing issues that affect the true significance levels.

Don't use t-tests to select the maximum lag for the VAR model - these test statistics won't even be asymptotically std.

The usual F-test for linear restrictions is not valid when testing for Granger causality, given the lags of the dependent variables that enter the model as regressors.

GRANGER CAUSALITY TESTING SERIES

If you are using a VAR model for purposes other than testing for Granger non-causality and the series are found to be cointegrated, the you would estimate a VECM model.If you are using a VAR model for other purposes, then you would use differenced data if the series are I(1), but not cointegrated.Don't fit the VAR in the differences of the data when testing for Granger non-causality.(You may still be wrong about there being no causality in the other direction.) If your data are not cointegrated, then you have no cross-check on your causality results. (This might occur if your sample size is too small to satisfy the asymptotics that the cointegration and causality tests rely on.) If you have cointegration and find one-way causality, everything is fine. So, if your data are cointegrated but you don't find any evidence of causality, you have a conflict in your results. "If two or more time-series are cointegrated, then there must be Granger causality between them - either one-way or in both directions. Finally, look back at what you concluded in Step 6 about cointegration.That is, a rejection supports the presence of Granger causality. Rejection of the null implies a rejection of Granger non-causality.The Wald test statistics will be asymptotically chi-square distributed with p d.o.f., under the null.They are there just to fix up the asymptotics.

It's essential that you don't include the coefficients for the 'extra' m lags when you perform the Wald tests.

Test the hypothesis that the coefficients of (only) the first p lagged values of X are zero in the Y equation, using a standard Wald test. Then do the same thing for the coefficients of the lagged values of Y in the X equation. For expository purposes, suppose that the VAR has two equations, one for X and one for Y.

Test for Granger non-causality as follows.

Now take the preferred VAR model and add in m additional lags of each of the variables into each of the equations.

It just provides a possible cross-check on the validity of your results at the very end of the analysis.

No matter what you conclude about cointegration at Step 6, this is not going to affect what follows.

If two or more of the time-series have the same order of integration, at Step 1, then test to see if they are cointegrated, preferably using Johansen's methodology (based on your VAR) for a reliable result.

If need be, increase p until any autocorrelation issues are resolved.

GRANGER CAUSALITY TESTING SERIAL

For example, ensure that there is no serial correlation in the residuals. Make sure that the VAR is well-specified.Specifically, base the choice of p on the usual information criteria, such as AIC, SIC. Determine the appropriate maximum lag length for the variables in the VAR, say p, using the usual methods.Most importantly, you must not difference the data, no matter what you found at Step 1. Set up a VAR model in the levels of the data, regardless of the orders of integration of the various time-series.If one is I(0) and the other is I(1), then m = 1, etc.

So, if there are two time-series and one is found to be I(1) and the other is I(2), then m = 2. Let the maximum order of integration for the group of time-series be m.Ideally, this should involve using a test (such as the ADF test) for which the null hypothesis is non-stationarity as well as a test (such as the KPSS test) for which the null is stationarity. Test each of the time-series to determine their order of integration.