A neural network enhanced volatility component model

Abstract

Volatility prediction, a central issue in financial econometrics, attracts increasing attention in the data science literature as advances in computational methods enable us to develop models with great forecasting precision. In this paper, we draw upon both strands of the literature and develop a novel two-component volatility model. The realized volatility is decomposed by a nonparametric filter into long- and short-run components, which are modeled by an artificial neural network and an ARMA process, respectively. We use intraday data on four major exchange rates and a Chinese stock index to construct daily realized volatility and perform out-of-sample evaluation of volatility forecasts generated by our model and well-established alternatives. Empirical results show that our model outperforms alternative models across all statistical metrics and over different forecasting horizons. Furthermore, volatility forecasts from our model offer economic gain to a mean-variance utility investor with higher portfolio returns and Sharpe ratio.

Keywords:

• Wavelet analysis
• ARMA process
• Volatility prediction
• Exchange rates

JEL:

• C63
• F47

Acknowledgments

We thank the Editor, Professor Jim Gatheral, and two anonymous referees for their helpful suggestions. We also thank Dr. Ying Jiang, participants at the China International Risk Forum in Shanghai Jiaotong University in 2017, and seminar participants at NYU Shanghai in 2018. All remaining errors are our own.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jia Zhai http://orcid.org/0000-0002-2746-7749

Yi Cao http://orcid.org/0000-0002-5087-8861

Xiaoquan Liu http://orcid.org/0000-0002-1765-4524

Notes

1 Launched in April 2005, the CSI 300 index represents the most comprehensive and widely followed index in the Chinese stock market. The index is based on the largest and most liquid A-shares in the Shanghai and Shenzhen Stock Exchanges and re-balanced every 6 months.

2 In the online appendix, we report statistical comparison between our model and the EGARCH model of Nelson (1991), the ARFIMA model of Granger (1980), and the HAR of Corsi (2009). The results are qualitatively the same.

3 We choose the ADF test because it is widely used in the literature although it is not the most powerful.

4 As a robustness check, we have used 5 neurons and 15 neurons and obtained qualitatively similar results. These are available from the authors upon request.

5 We aggregate volatility forecasts over all six horizons for each asset in order to provide a comprehensive and clear picture.

We also conduct the Mincer and Zarnowitz (1969) regression, which shows the ability of the forecasted volatility in explaining the true volatility proxy. We find that the $R^2$ decreases massively with increasing forecast horizons for all models as expected. However, our proposed Hybrid model still shows 30% to 70% explanatory power for the longest forecast horizon and comes out stronger than the competing models. These results are available upon request from the authors.

7 It is worth noting that the artificial neural network does not work well on modeling and forecasting the overall volatility dynamics. See Yao et al. (2017) for example.

8 We have conducted yet another robustness check by adopting the low-pass Hodrick and Prescott (1997) filter and see whether the performance of the Hybrid model is due to our choice of the particular decomposition method, i.e. the wavelet method. We obtain qualitatively similar results that the model with the Hodrick and Prescott (1997) filtering, with the long-/short-term component still modeled via the artificial neural network and the ARMA process, respectively, outperforms the HSY and EL models. The results are available from the authors upon request.

9 These results are not reported to conserve space. They are available upon request from the authors.