I have the following CUSUM test resulted from autoregressive distributed lag models (ARDL). Does the CUSUM results show that the model is stable? I am a bit confused because the red line in CUSUM square have only slightly crossed the 5% significance level boundaries .
The answer is not trivial. The fact that two or more test about the same hypothesis, parameters stability in this case, give you different (also opposite) results is not uncommon. Basically the problem came from the fact that you do not know the source of potential instability. One test is more power than the other in some case but the opposite is true in others.
If your dataset go to infinity and the true parameters are stable, the tests should return the same result (refuse instability). However in finite sample your problem can appear. In small dataset is frequent.