Before revision:  The realized moments of the return are unbiased and relative efficient estimators for the actual moments of the return distribution under a martingale condition in the return process. For the estimation of a stochastic volatility model , we employ a simple method of estimation and a generalized method of moments estimation based on the realized second and third moments . Conditional thin tale property of the return distribution with given quadratic variation of the return is discussed.
After revision:  The realized moments of the return are unbiased and relative efficient estimators for the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use a square root stochastic volatility model for the derivations of moment conditions for estimations. Using the S\&P 500 index high frequency data, the realized versions of the moment variations is used for the estimation of a stochastic volatility model , we employ a simple method of estimation and a generalized method of moments estimation based on the realized second and third moments . Conditional thin tale property of the return distribution with given quadratic variation of the return is discussed.