### What if first differences co-integrate?

Posted:

**Sun Sep 15, 2019 7:52 am**Hello!

I'm busy with VAR/ECM models with five variables describing stocks and flows of uenmployed job seekers and vacant jobs (for a matching function). All these series seem to be integrated I(1) or higher. However, the results of pretests (ADF, Phillips-Perron, KPSS) are partially mixed, and two of the variables might be I(2). I think this invalidates Johansen cointegration tests that requires orders of integration to bbe the same. The results of Johansen test is sensitive to lag structure and assumptions on exogenous variables (constant, trend). On the other hand ARDL model and coint-test (bounds test) suppose there is only one cointegrating relation, but this test requires variables I(0) or I(1). The latter method gives more credible results for matching function as a long run equilibrium. Whatever, I happened to run VAR and ARDL models with (first) differenced variables and find strong evidence for co-integration. I wonder if applying ARDL is okay, because the differenced variables are either I(0) or I(1)? How can you interpret this case where first differences seem stationary but co-integrate strongly? Does this mean that variables are I(2)?

Kind regards

Mark

I'm busy with VAR/ECM models with five variables describing stocks and flows of uenmployed job seekers and vacant jobs (for a matching function). All these series seem to be integrated I(1) or higher. However, the results of pretests (ADF, Phillips-Perron, KPSS) are partially mixed, and two of the variables might be I(2). I think this invalidates Johansen cointegration tests that requires orders of integration to bbe the same. The results of Johansen test is sensitive to lag structure and assumptions on exogenous variables (constant, trend). On the other hand ARDL model and coint-test (bounds test) suppose there is only one cointegrating relation, but this test requires variables I(0) or I(1). The latter method gives more credible results for matching function as a long run equilibrium. Whatever, I happened to run VAR and ARDL models with (first) differenced variables and find strong evidence for co-integration. I wonder if applying ARDL is okay, because the differenced variables are either I(0) or I(1)? How can you interpret this case where first differences seem stationary but co-integrate strongly? Does this mean that variables are I(2)?

Kind regards

Mark