Before revision: We study the probabilistic and statistical properties of the variation based realized third and fourth moments of financial returns . 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.
After revision: We study the probabilistic and statistical properties of the variation based realized third and fourth moments of financial returns as estimators of the actual moments of the return distribution under a martingale condition in the return process.