Hi! If an unstable cumulative sum of recursive residuals squared (CUSUMSQ) test indicate instability in the residuals of, say an ARDL model, can this be remedied by the use of heteroscedasticity robust (HAC) standard errors?
I would say yes because CS is designed a test for parameter and variance shifts. Note that Robust doesn’t mean that it Is applicable to all types of heterosk but it doesn’t hurt to try. For me, I would first attempt to identify the missing variable and achieve stability. You can even recreate the equation once you have known of the long run coefficients and then bring it into the OLS framework where you can do all times of things. Within the ARDL you are controlled by the flowchart of the ARDL subroutine