Before you conduct a formal test, it may be useful to simply plot the data series (or/and estimated errors) for 'eyeballing'. The choice of the appropriate orders for the AR/MA terms is an important issue. It may depend on a number of factors including data frequency. I would suggest you to use all kinds of diagnostic tests, both formal and informal, before you decide on your model estimation.

It is highly unlikely to defend a goal when you don't have a goalkeeper, similarly without finding enough evidence for the presence of ARCH effects, running any ARCH- GARCH models will not be conclusive. Therefore, It will be appropriate to correct the base model first for any improvements as pointed out in the above comment.

Thank You Very much for your valuable and constructive comments. I am trying to check my base model and cross check the results with other tests. Will soon post results.