Two questions on the Engle-Granger method of cointegration.
1: Should I use the Pantula method for trend specification for EG cointegration? Intuitively, it seems better to go from top to bottom - with trend and constant first, and then go down to constant if trend is insignificant etc?
2: Do Engle-Granger residuals need to be normally distributed to be of use (assuming they are stationary)?
We have to rely on the statistical literature and monte carlo studies. The common practice is G-to-S with t=I.6 criteria for eliminating a lag (see Ng and Perron in the Journal of American statistical Association). Normality has little effect. Another point here is that it is a waste of time using Pantula principle here. Do all in one equation and eliminate based on 1.6 criterion Alternatively, regress out the constant and trend and only work with delta residual on residual(-1) etc.
Thanks Chuck! By "G-to-S with t=I.6 criteria", you mean eliminating variables with a t-value below 1.6?
Yes thats what i mean, but you pick a maximum value for example lag 8 and then you drop the 8th lag if the t is below 1.6 in absolute value and then you stop if for example the 6th lag has a t value greater than 1.6 in absolute value. Ensure that the maximum lag does not have auto correlation when you select the maximum lag.
The Engle-Granger test statistic for cointegration reduces to an ADF unit root test of the residuals of the cointegration regression: If the residuals contain a unit root, then there is no cointegration. The null hypothesis of the ADF test is that the residuals have a unit root.
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