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I am testing for cointegration all the pairs from a set of 100 stocks. I run an Ordinary Least Square Regression on each pair and then I test for the existence of unit roots in the residuals. I am using the ADF test with no trend and no intercept. I am surprised that I found a big amount of pairs which the test on the residual rejected the null hypothesis of having a unit root, with p-values smaller than 0.01. Can I use the Dick Fuller Statistic to rank those pairs? All the series have the same length.

Ferdi
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Thiago Steiner Alfeu
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  • It depends on what you are after. ADF test tells you how strongly you can reject the null hypothesis of a unit root, so if you want to rank the pairs by how strongly you reject the null, then sure. – Akavall Jul 01 '12 at 12:40
  • I would think that as long as you validated the Gaussian Assumptions underlying the t test you should be good to go. I am currently expanding the ECM solution to deal with Gaussian Assumptions/Violations using AUTOBOX a time series / econometric package I helped develop. – IrishStat Jul 01 '12 at 15:27
  • @Akavall, I want to rank them by how strong they are cointegrated. As the pairs are very different, have different statistical caracteristics, i was not sure if a DF t-statistic for one pair could be comparable with a t-statistic for another pair. – Thiago Steiner Alfeu Jul 01 '12 at 19:19
  • @IrishStat, thank you. I agree with you that validating the Gaussian Assumptions is a very important matter in dealing with the t statistic. How should I validate those assumptions? – Thiago Steiner Alfeu Jul 01 '12 at 19:29
  • @Thiago Please see my answer to http://stats.stackexchange.com/questions/31275/how-can-i-check-if-my-time-series-data-is-zero-mean-stationary-and-independent – IrishStat Jul 01 '12 at 19:41
  • @Thiago In addition the errors from the model should have an auto-correlation function suggesting randomness. – IrishStat Jul 01 '12 at 20:03
  • @IrishStat Thank you for your valuable and helpfull answer! – Thiago Steiner Alfeu Jul 02 '12 at 18:46

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