I want to apply multivariate GARCH(DCC-GARCH) for 2 variables (rbse, roil) to know the spillover effect. As a precondition, I have to test the presence of ARCH effect in the residuals of linear model. which linear model I should use to get the residuals for arch test... should I use 2 different equations , rbse = c + rbse(-1) and roil= c+ roil(-1) OR I should use the equation roil= c + rbse.

I think, since in multivariate GARCH we study effect of roil on rbse , the residuals we should check is for the third equation. BUT in many papers using MGARCH, authors are reporting results of arch effect differently for the 2 variables meaning that they are using equation 1 and 2. why so.. pls comment