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Asymptotic properties of the realized skewness and related statistics

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Abstract

The recent empirical works have 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.

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Notes

  1. Neuberger (2012) uses the term realized skewness for a different concept.

  2. Recall that, for a locally square-integrable martingale M such that \(M_0=0\), \(\langle M\rangle \) denotes the predictable quadratic variation of M, i.e., the predictable increasing process such that \(M^2-\langle M\rangle \) is a local martingale (such a process always exists and is unique; see e.g., Theorem 4.2 from Chapter I of Jacod and Shiryaev (2003).

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, 153-8914, Japan

    Yuta Koike

  2. Department of Business Administration, Graduate School of Social Sciences, Tokyo Metropolitan University, Tokyo, 100-0005, Japan

    Yuta Koike

  3. The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan

    Yuta Koike

  4. CREST, Japan Science and Technology Agency, Kawaguchi, 333-0012, Japan

    Yuta Koike

  5. Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, 999078, China

    Zhi Liu

Authors
  1. Yuta Koike
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  2. Zhi Liu
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Corresponding author

Correspondence to Zhi Liu.

Additional information

The authors would like to thank the Editor, the Association Editor and two anonymous referees for their very extensive and constructive suggestions that helped to improve the paper considerably. Koike’s work is partially supported by JSPS KAKENHI Grant Numbers JP16K17105, JP17H01100; Liu’s work is partially supported by FDCT of Macau (No. 078/2013/A3 and No. 202/2017/A3) and NSFC (No. 71471173).

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Koike, Y., Liu, Z. Asymptotic properties of the realized skewness and related statistics. Ann Inst Stat Math 71, 703–741 (2019). https://doi.org/10.1007/s10463-018-0659-8

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  • DOI: https://doi.org/10.1007/s10463-018-0659-8

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