Realized higher-order comoments

We propose a new realized third-order comoment and new realized fourth-order joint cumulants, which are standardized comoments. They are obtained from sub-period returns and lower-order comoments and satisfy A. Neuberger's (Realized skewness. Rev. Financ. Stud., 2012, 25(11), 3423-3455) aggregation property. Different from other realized higher-order comoments obtained from sub-period returns only, those in this study reflect characteristics of the volatility of volatility as well as jump contributions. As a result, our realized kurtosis and coskewness can reflect well-known phenomena such as the positive autocorrelation of volatility or negative correlation between returns and covariances.