Dear Professors,

I have been thinking recently about the possibility of combining F-test or Chi-square test statistics from two different regression models to see their joint significance. Particularly, let's say I have two ARDL models with bound test values of 5.67 and 6.23 with k1 and k2 degrees of freedom. I would like to know if it is possible to have a test or a way to combine these two statistics to conclude their joint significance. 

Please, advise me.