Asymptotic properties of the realized skewness and related statistics

TL;DR

This paper investigates the asymptotic behavior of realized skewness, a high-frequency financial statistic, providing theoretical insights and estimation methods under measurement errors and stochastic sampling times.

Contribution

It offers a rigorous analysis of the asymptotic properties of realized skewness and develops an estimation framework accounting for measurement errors and stochastic sampling.

Findings

Asymptotic distribution of realized skewness derived

Estimation methods for skewness with measurement errors proposed

Theoretical foundation for using realized skewness in forecasting

Abstract

The recent empirical work of Amaya et al. (2015) has pointed out that the realized skewness, which is the sample skewness of intraday high-frequency returns of a financial asset, serves as forecasting future returns in the cross-section. Theoretically, the realized skewness is interpreted as the sample skewness of returns of a discretely observed semimartingale in a fixed interval. The aim of this paper is to investigate the asymptotic property of the realized skewness in such a framework. We also develop an estimation theory for the limiting characteristic of the realized skewness in a situation where measurement errors are present and sampling times are stochastic.