How Should We Interpret Evidence of Time Varying Conditional Skewness?

Abstract

Several recent articles report evidence of predictability in the skewness of equity returns, raising hopes that predictability in third moments will be useful for forecasting the probability of tail events. The evidence is unfortunately difficult to interpret, partly because they were obtained mainly from parametric models of time-varying conditional skewness, and because little is known about the behavior of such models, for instance, when there are outliers. We investigate a non-parametric approach to testing for predictability in skewness. Specifically, we explore the size and power of a Runs tests, and compare this approach with other tests. A re-examination of daily market returns reveals mild evidence of predictability in skewness. Incorporating this conditional heteroskewness into standard volatility models hardly improves out-of-sample forecasts of tail probabilities.

Keywords: Conditional skewness, Runs test, ARCD model, Hansen t, heteroskewness, heterokurtosis, third moments, time-varying higher moments

JEL Classification: C5, C12