Testing for cointegration: Johansen vs Dickey-Fuller

Hi

First of all, when dealing with time series, having contradictory 
results is not the exception but almost the rule! You may have opposite 
results between tests, with a same test with different specifications 
and finally with same test, same specification but different number of lags!

Your contradictory results come maybe from the way you apply the DF 
test, as pointed out by Jae Kim. In the residual based approach (or 
"Engle and Granger", or "two steps"), one applies unit root tests on the 
residuals from the cointegrating vector. If this cointegrating vector is 
known (from theory), just use the ADF.

Nevertheless, if the cointegrating vector has to be estimated (with 
usual OLS, as you did), one has to take into account this uncertainty 
and correct the distribution (which is then "larger") what EG did with 
Monte-Carlo, and Philips and Ouliaris more theoretically. The last one 
is implemented  in package urca under ca.po.

So maybe your two favorable result come from the fact that you estimate 
the cointegrating value but then take it as known a priori. Note 
nevertheless that studying spreads one typically assumes the vector (1, 
-1).

Small point, as residuals from a regression have zero mean, I don't 
think you need to test a model with a drift.

Finally, for your data, you may be interested in testing for threshold 
cointegration, that is, cointegration and error correction occurring 
only when deviations from long-run are big enough, which is more 
realistic and theory consistent. Some functions (as for your case a test 
of no cointegration against threshold cointegration with known vector) 
are availabe in dev version of package tsDyn (see TVECM_SeoTest).

Matthieu

Jae Kim a ?crit :

Testing for cointegration: Johansen vs Dickey-Fuller

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