Volatility forecasting by quantile regression

Abstract

Quantile regression allows one to predict the volatility of time series without assuming an explicit form for the underlying distribution. Financial assets are known to have irregular return patterns; not only the volatility but also the distribution functions themselves may vary with time, so traditional time series models are often unreliable. This study presents a new approach to volatility forecasting by quantile regression utilizing a uniformly spaced series of estimated quantiles. The proposed method provides much more complete information on the underlying distribution, without recourse to an assumed functional form. Based on an empirical study of seven stock indices, using 16 years of daily return data, the proposed approach produces better volatility forecasts for six of the seven indices.

Acknowledgements

This research was partly supported by the National Science Council of Taiwan (NSC95-2415-H-155-004). The author thanks the referees for valuable comments and Wen-Cheng Hu, Chin-Chun Chen and Sassa Lin for providing excellent research assistance.

Notes

¹ A detailed survey can be found in Ghysels et al. (1996).

² Please see Carr et al. (2003) and Wu (2008).

³ A detailed survey is given in Poon and Granger (2003).

⁴ A detailed survey can be found in Pearson and Tukey (1965).

⁵ Some other VaR approaches are also included in his study for purposes of comparison, including historical simulation, EWMA and IGARCH.