I am trying to estimate the long-run relationship between equity prices and bond default risk measures using a 250*250 panel of firms. There is strong theoretical evidence that there is a relationship between the two, so I expected cointegration to exist. I have used Hadri, Fisher and IPS unit root tests to check the order of integration of my dependent / independent variables; the Hadri test rejects the null that all panels are stationary very convincingly, but the other tests also reject the H0 of unit roots with a p value of 0. Therefore I conclude that some panels contain stationary variables and others unit root variables. How should I approach testing / estimating the cointegration? I have used Pedroni and Westerlund tests to check for cointegrating relationships, and conclude that cointegration exists based on this test. But I am concerned because two I(0) variables cannot cointegrate, and the order of integration of vars in each panel is questionable.

How should I proceed? I do not know which panels contain stationary/nonstationary series - or in what percentage of my panels the series are not of the same order of integration. Are the above cointegration tests valid in this context? Should I just assume, based on theory, that cointegrating relationships should exist and proceed with this assumption?

Thank you in advance for your generous help.


  • $\begingroup$ 250*250 means 250 firms observed over 250 time periods? $\endgroup$ – mpiktas Dec 20 '15 at 19:08
  • $\begingroup$ Yes, 250 firms for 250 days. $\endgroup$ – Robert Brown Dec 20 '15 at 19:11
  • $\begingroup$ To do some shameless self-promotion: You can apply tests that allow you to classify series as I(0)/I(1). See here. $\endgroup$ – Christoph Hanck Dec 21 '15 at 5:29

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