Volatility Research and Forecast on CSI 300 Index Futures byUsing the ARMA-GARCH-SN Model

doi:10.12005/orms.2018.0097

Abstract

Abstract: By using the high frequency data(two deals per second) of five trading days in CSI 300 index futures, this paper mainly studies the intraday volatility characteristics of the CSI 300 stock index futures and forecasts the intraday volatility. The results show that the intraday yield of high frequency stock index futures has obvious volatility aggregation and AutoRegressive Conditional Heteroscedasticity(ARCH)effect, but there is no peak and fat-tailed phenomenon. The distribution of the return series accords with a skewed normal distribution. So the optimal ARMA-GARCH-SN model is established, and the adequacy of the model fit is verified. The fitting results show that ARMA(1,2)-GARCH(1,1)-SN can well describe the characteristics of ultrahigh frequency intraday volatility of CSI 300 index futures, the impact on the conditional variance has a strong persistence, and long memory effect is found in the intraday volatility. Finally, two steps of the return rate and the volatility are predicted by the bootstrap method. We also use the rolling regression forecasting method to do the in-sample prediction. The prediction results show that the volatility prediction can reflect the intraday volatility characteristics of the stock index futures commendably.

Key words: high-frequency data, ARMA-GARCH-SN model, CSI 300 index futures, intraday pattern, forecast

摘要： 运用五个交易日的股指期货高频数据(每秒两笔),本文主要研究了沪深300股指期货日内波动率特征并对日内波动率预测。研究发现高频股指期货日内收益率有明显的波动率聚集和条件异方差现象,但无尖峰厚尾现象,收益率序列分布符合有偏正态分布。因此,我们对时间序列建立了最优的ARMA-GARCH-SN模型,并对模型拟合充分性做了验证,拟合结果发现ARMA(1,2)-GARCH(1,1)-SN模型基本能够刻画股指期货高频日内波动特征,条件方差所受的冲击具有很强的持续性、日内波动也具有长记忆性,最后我们还利用自助法对高频股指期货日内波动率两步预测、利用滚动回归预测方法对样本做了样本内预测。预测结果表明,波动率预测结果能够较好地反映股指期货日内波动特征。

关键词: 高频数据, ARMA-GARCH-SN模型, 沪深300股指期货, 日内模式, 预测

CLC Number:

F830.91

WANG Shu-sheng, WANG Jun-bo, XU Tong-tong, YU Zheng. Volatility Research and Forecast on CSI 300 Index Futures byUsing the ARMA-GARCH-SN Model[J]. Operations Research and Management Science, 2018, 27(4): 153-161.

王苏生, 王俊博, 许桐桐, 余臻. 基于ARMA-GARCH-SN模型的沪深300股指期货日内波动率研究与预测[J]. 运筹与管理, 2018, 27(4): 153-161.

References

[1]Engle R F. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[J]. Econometrica: Journal of the Econometric Society, 1982. 4(50): 987-1007.
[2]Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Eeri Research Paper, 1986, 31(3): 307-327.
[3]Nelson D B. Conditional heteroskedasticity in asset returns: a new approach[J]. Econometrica, 1991, 59(2): 347-70.
[4]Engle R F, Bollerslev T. Modelling the persistence of conditional variances[J]. Econometric Reviews, 1986, 5(1): 1-50.
[5]Chou R Y. Volatility persistence and stock valuations: Some empirical evidence using garch[J]. Journal of Applied Econometrics, 1988, 3(3): 279-94.
[6]Bollerslev T P, Engle R F, Wooldridge J M. A capital asset pricing model with time varying covariance[J]. Journal of Political Economy, 1988. 96(1): 116-31.
[7]Jagannathan R, Glosten L R, Runkle D E. “On the relation between the expected value and volatility of the nominal excess return on stocks”[J]. The Journal of Finance, 1993. 48(5): 1779-1801.
[8]Engle R F, Kroner K F. Multivariate simultaneous generalized ARCH[J]. Econometric theory, 1995, 11(1): 122-150.
[9]Curto J D, Pinto J C, Tavares G A N. Modeling stock markets’ volatility using GARCH models with Normal, Student’s and stable Paretian distributions[J]. Statistical Papers, 2009, 50(2): 311-321.
[10]Liu H, Shi J. Applying ARMA-GARCH approaches to forecasting short-term electricity prices[J]. Energy Economics, 2013. 37: 152-166.
[11]Bildirici M, Ersin Ö. Modeling markov switching ARMA-GARCH neural networks models and an application to forecasting stock returns[J]. The Scientific World Journal, 2014. 2014(3): 21.
[12]Tian S, Hamori S. Modeling interest rate volatility: a realized GARCH approach[J]. Journal of Banking & Finance, 2015. 61: 158-171.
[13]Laurent S, Lecourt C, Palm F C. Testing for jumps in conditionally Gaussian ARMA-GARCH models, a robust approach[J]. Computational Statistics & Data Analysis, 2016, 100: 383-400.
[14]Akar C, Çiçek S. “New” monetary policy instruments and exchange rate volatility[J]. Empirica, 2016. 43(1): 141-165.
[15]Righi M B, P.S. Ceretta P S. Forecasting value at risk and expected shortfall based on serial pair-copula constructions[J]. Expert Systems with Applications, 2015. 42(17): 6380-6390.
[16]萧楠.ARMA-GARCH模型对上海铜期货市场收益率的建模与分析[J].运筹与管理,2006,15(5):128-132.
[17]黄海南与钟伟, GARCH类模型波动率预测评价[J].中国管理科学,2007,15(6):13-19.
[18]惠军,朱翠.证券投资基金市场的ARMA-ARCH类模型分析[J].合肥工業大學學報:自然科學版,2010,33(7):1108-1112.
[19]方世建,韩宇.基于变换核密度估计的半参数GARCH模型[J].系统工程理论与实践,2014,34(8):1963-1970.
[20]曹栋,张佳.基于GARCH-M模型的股指期货对股市波动影响的研究[J].中国管理科学,2017,25(1):27-34.
[21]Tsay R S, Tiao G C. Consistent estimates of autoregressive parameters and extended sample autocorrelation function for stationary and nonstationary ARMA models[J]. Journal of the American Statistical Association, 1984, 79(385): 84-96.
[22]Engle R F, Bollerslev T. “Modeling the persistence of conditional variances”[J]. Econometric Reviews, 1986, 5(1): 1-50.
[23]Pascual L, Romo J, Ruiz E. Bootstrap prediction for returns and volatilities in GARCH models[J]. Computational Statistics & Data Analysis, 2006, 50(9): 2293-2312.