Skewness and Kurtosis Persistence: Conventional vs. Robust Measures

Recently, independent of each other, there has been interest in (i) time-variation in higher-order moments; (ii) idiosyncratic skewness and predictability of skewness in the asset pricing context; and (iii) robust measures of skewness and kurtosis. The second literature questions the usefulness of past skewness as a predictor of future skewness, arguing that skewness may not exhibit strong enough persistence. We look at an intersection of these three literatures and study the persistence (in the time-series) of conventional and robust measures of higher-order moments for eight financial series. Conventional and robust measures, when the moments exist, are highly correlated. Furthermore, robust skewness and kurtosis measures exhibit as much or more persistence as the conventional measures. The results suggest that one could consider robust measures, instead of the conventional measures, in the asset pricing context.