Because of the above mentioned Davies’ problem, the classical tests F1 and F2 have non-standard distributions. Many authors have examined the Davies’ problem, for example, Andrews and Ploberger (1994) and Hansen (1996). In general, the construction of critical values for these distributions of test statistics is non-trivial (Andrews and Ploberger, 1994) and bootstrapping becomes the only realistic alternative. Following Hansen (2000; 2017), we propose to use a parametric bootstrap procedure in the tradition of Hansen (1996) to construct the p-values of the proposed tests. More specifically, the following algorithm is used.