This paper considers GMM estimation of autoregressive processes. It is shown that, contrary to the case where the noise is independent (see Kim, Qian and Schmidt (1999)), using high-order moments can provide substantial efficiency gains for estimating the AR(p) model when the noise is only uncorrelated.
Broze, L., Francq, C., & Zakoian, J.-M. (2000). Non redundancy of high order moment conditions for efficient GMM estimation of weak AR processes (CORE Discussion Papers 2000/33). https://hdl.handle.net/2078.5/35524