Test for no ARCH effects

[T27667]

If you are going to test for no arch effects up to 2 lags, say, for a sample of T=3572 residuals, e, is the approach then the following:
Calculate the test statistics T*R^2 where R^2 is the coefficient of determination from the regression
e^2(T) = a+b*e^2(T-1)+c*e^2(T-2) <=>
e^2(3572) = a+b*e^2(3571)+c*e^2(3570)
and then compare T*R^2 in Chi^2 with 2 degrees of freedom? Is that really it?