Forecasting the Chinese stock market volatility: A regression approach with a t-distributed error

ABSTRACT

In this paper, we improve the ordinary least squares (OLS) estimation approach by replacing a normally distributed error with a t-distributed error. Empirically, we investigate the predictability of the Chinese stock market volatility based on this modified approach. Results show that the modified OLS method with a t-distributed error has a significantly stronger forecasting power than its counterpart with a normally distributed error. From an asset allocation perspective, the modified OLS approach can help a mean-variance investor obtain sizeable utility gains. We also conduct two extended empirical analyses and further verify the superiority of the regression approach with a t-distributed error. Our results are robust to a series of settings. Finally, we find that the regression approach with a t-distributed error shows greater tolerance for outliers by assigning smaller weights to them, thereby highlighting its superior performance.

JEL CLASSIFICATION:

• C53
• C58
• G11
• G17

KEYWORDS:

• Chinese stock market
• measurement errors
• outliers
• t-distribution
• volatility forecasting

Acknowledgments

The authors are grateful to the editor, Mark Taylor, and an anonymous reviewer of this journal for their constructive comments that contributed to the improvement of this paper. We thank seminar participants at Nanjing University of Science and Technology, Southwest Jiaotong University for helpful comments and suggestions. We are solely responsible for any error that might yet remain.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Specifically, the RV is positively skewed and leptokurtic.

2 Undeniably, the logarithmic RV can improve the efficiency of OLS estimators. Nevertheless, the logarithmic RV is only close to a normal distribution. Sakata and White (1998) argue that the reliability of OLS estimators can be undermined by a small number of outliers.

3 To reduce computational complexity, we fix the degrees of freedom to 1 for t_n. For the robustness, we consider degrees of freedom that vary adaptively over time and obtain qualitatively similar results.

4 The website is https://realized.oxford-man.ox.ac.uk/.

5 The results remain qualitatively similar when we use the semi-quadratic statistic or circular block bootstrap.

6 See Rapach, Ringgenberg, and Zhou (2016) for more details about the measurement of longer-horizon economic value.

7 The asymmetric return $r_t^{-}=min(r_t,0)$.

8 Theoretically, the DoC rate of the random walk is 50%.

9 We thank an anonymous referee for this constructive suggestion.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [72001110 to Y. Zhang; 71901122 to D. Wen; 71722015, 72071114 to Y. Wang], the Fundamental Research Funds for the Central Universities [30919013232 to Y. Zhang; 30919013204 to D. Wen], the Research Fund for Young Teachers of School of Economics and Management, NJUST [JGQN2009 to Y. Zhang]