I often use the ARDL Bounds testing approach and I am of the opinion that if the number of lags used is from 1 to the optimal lag length (at least not exceeding the optimal number of lags) both Durbin Watson (test for 1st order autocorrelation) and Breusch-Godfrey (test for higher-order autocorrection) should be okay for you not to reject both null hypotheses.
It matters because the major assumption in ARDL is that enough lags have been used to handle endogeneity and autocorrelation. Please see my paper in IREF "A convenient method of obtaining ARDL estimates and test statistics .........." and also can be found in RG.
In Pesaran's orginial study, M. HASHEM PESARAN, YONGCHEOL SHIN AND RICHARD J. SMITH, 'BOUNDS TESTING APPROACHES TO THE ANALYSIS OF LEVEL RELATIONSHIPS'JOURNAL OF APPLIED ECONOMETRICS
J. Appl. Econ. 16: 289–326 (2001), explains ton page 314, footnote 37 why the issue of serial correlation does not matter in ARDL approach. Good luck, All the best;
MUSTAFA is wrong or more appropriately stated appears to have misunderstood footnote 31 of PSS (2001). Indeed, serial correlation is crucial in ARDL estimation. In the paper he cited by PSS(2001) on page 308, the authors write "it is, therefore, important that the lag order p of the underlying VAR is selected APPROPRIATELY. There is a delicate balance between choosing p sufficiently large to mitigate the residual correlation problem ....available" Serial correlation is mentioned 5 times in that paper which shows that it matters. Their statement on page 314, footnote 37 assumes that the order of the ARDL is appropriately augmented by the suitable specification of the lag structure of the dependent and independent variables-- see page 311 and 312 (bottom). These augmentations are intended to suck away serial correlation and endogeneity from the model. For other examples, see Pesaran (1997, pp. 182-185 and Pesaran and Shin (1999, pp381-387; 404-405)
When I'am using Ardl method, I always check the bound test of fisher, and if it's okay, I will do the residual diagnostics to check if the model possess white noise error, without autocorrelation and without heteroskedasticity, so if I have a problem with these tests, I won't accept the model and I will re-estimate the model with another new exogenous variables or I try to create factors between two variables (maybe due the colinearity problem)