# Estimation of variance in GMM

In GMM, the efficient weight matrix minimizes the asymptotic variance of the GMM estimator by setting:

$$W_T^{opt} = S_T^{-1}$$

where $$S_T$$ is an estimator of the asymptotic variance of the moments, $$S = Var(\sqrt{T}g_T(\beta))$$.

In my textbook, it says:

How to estimate $$S_T$$ depends on whether the moments are:

1. IID over time
2. independent over time, but heteroskedastic
3. autocorrelated and heteroskedastic over time

My question is: how do we test in which of the three cases we are?