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Forecasting the Chinese stock volatility across global stock markets

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  • Liu, Jing
  • Ma, Feng
  • Zhang, Yaojie

Abstract

In view of the growing concern of Chinese stock fluctuation, this paper forecasts the Chinese stock volatility by extracting global stock information by combining forecasts of time-varying parameter (TVP) volatility models. First, we construct individual constant coefficient (CC) models and TVP models across 27 global stock markets, and then use several strategies to combine their forecasts. The results show global stock information does forecast the future volatility of Chinese stock market. Both the forecast accuracy and economic values can be further improved by using strategies combining TVP models with global stock information. Specifically, the median combination shows its superiority for the volatile Chinese stock market. Our findings are robust to different estimation window sizes, volatility proxies, and evaluation criteria.

Suggested Citation

  • Liu, Jing & Ma, Feng & Zhang, Yaojie, 2019. "Forecasting the Chinese stock volatility across global stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 466-477.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:466-477
    DOI: 10.1016/j.physa.2019.03.097
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    as
    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
    3. Chun Liu & John M. Maheu, 2008. "Are There Structural Breaks in Realized Volatility?," Journal of Financial Econometrics, Oxford University Press, vol. 6(3), pages 326-360, Summer.
    4. Corsi, Fulvio & Pirino, Davide & Renò, Roberto, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Journal of Econometrics, Elsevier, vol. 159(2), pages 276-288, December.
    5. Gong, Xu & Lin, Boqiang, 2018. "The incremental information content of investor fear gauge for volatility forecasting in the crude oil futures market," Energy Economics, Elsevier, vol. 74(C), pages 370-386.
    6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    7. Feng Ma & M. I. M. Wahab & Jing Liu & Li Liu, 2018. "Is economic policy uncertainty important to forecast the realized volatility of crude oil futures?," Applied Economics, Taylor & Francis Journals, vol. 50(18), pages 2087-2101, April.
    8. Tian, Fengping & Yang, Ke & Chen, Langnan, 2017. "Realized volatility forecasting of agricultural commodity futures using the HAR model with time-varying sparsity," International Journal of Forecasting, Elsevier, vol. 33(1), pages 132-152.
    9. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    10. Andersen, Torben G. & Dobrev, Dobrislav & Schaumburg, Ernst, 2012. "Jump-robust volatility estimation using nearest neighbor truncation," Journal of Econometrics, Elsevier, vol. 169(1), pages 75-93.
    11. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    12. Yi, Yongsheng & Ma, Feng & Zhang, Yaojie & Huang, Dengshi, 2018. "Forecasting the prices of crude oil using the predictor, economic and combined constraints," Economic Modelling, Elsevier, vol. 75(C), pages 237-245.
    13. Li, Hongquan & Hong, Yongmiao, 2011. "Financial volatility forecasting with range-based autoregressive volatility model," Finance Research Letters, Elsevier, vol. 8(2), pages 69-76, June.
    14. Wei, Yu & Wang, Peng, 2008. "Forecasting volatility of SSEC in Chinese stock market using multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(7), pages 1585-1592.
    15. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    16. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
    17. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    18. Christopher J. Neely & David E. Rapach & Jun Tu & Guofu Zhou, 2014. "Forecasting the Equity Risk Premium: The Role of Technical Indicators," Management Science, INFORMS, vol. 60(7), pages 1772-1791, July.
    19. Ma, Feng & Liu, Jing & Huang, Dengshi & Chen, Wang, 2017. "Forecasting the oil futures price volatility: A new approach," Economic Modelling, Elsevier, vol. 64(C), pages 560-566.
    20. Barbara Rossi & Atsushi Inoue, 2012. "Out-of-Sample Forecast Tests Robust to the Choice of Window Size," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 432-453, April.
    21. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, August.
    22. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    23. Peng, Huan & Chen, Ruoxun & Mei, Dexiang & Diao, Xiaohua, 2018. "Forecasting the realized volatility of the Chinese stock market: Do the G7 stock markets help?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 78-85.
    24. Xu Gong & Boqiang Lin, 2018. "Structural breaks and volatility forecasting in the copper futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(3), pages 290-339, March.
    25. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    26. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    27. Yu, Honghai & Fang, Libing & Sun, Wencong, 2018. "Forecasting performance of global economic policy uncertainty for volatility of Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 931-940.
    28. Liu, Jing & Wei, Yu & Ma, Feng & Wahab, M.I.M., 2017. "Forecasting the realized range-based volatility using dynamic model averaging approach," Economic Modelling, Elsevier, vol. 61(C), pages 12-26.
    29. Jayech, Selma, 2016. "The contagion channels of July–August-2011 stock market crash: A DAG-copula based approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 631-646.
    30. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    31. Engel, Charles, 1994. "Can the Markov switching model forecast exchange rates?," Journal of International Economics, Elsevier, vol. 36(1-2), pages 151-165, February.
    32. Ma, Feng & Liu, Jing & Wahab, M.I.M. & Zhang, Yaojie, 2018. "Forecasting the aggregate oil price volatility in a data-rich environment," Economic Modelling, Elsevier, vol. 72(C), pages 320-332.
    33. Ahoniemi, Katja & Lanne, Markku, 2013. "Overnight stock returns and realized volatility," International Journal of Forecasting, Elsevier, vol. 29(4), pages 592-604.
    34. David E. Rapach & Jack K. Strauss & Guofu Zhou, 2010. "Out-of-Sample Equity Premium Prediction: Combination Forecasts and Links to the Real Economy," Review of Financial Studies, Society for Financial Studies, vol. 23(2), pages 821-862, February.
    35. Molodtsova, Tanya & Papell, David H., 2009. "Out-of-sample exchange rate predictability with Taylor rule fundamentals," Journal of International Economics, Elsevier, vol. 77(2), pages 167-180, April.
    36. Markwat, Thijs & Kole, Erik & van Dijk, Dick, 2009. "Contagion as a domino effect in global stock markets," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 1996-2012, November.
    37. Gong, Xu & Lin, Boqiang, 2017. "Forecasting the good and bad uncertainties of crude oil prices using a HAR framework," Energy Economics, Elsevier, vol. 67(C), pages 315-327.
    38. Zhou, Xiangyi & Zhang, Weijin & Zhang, Jie, 2012. "Volatility spillovers between the Chinese and world equity markets," Pacific-Basin Finance Journal, Elsevier, vol. 20(2), pages 247-270.
    39. Mensi, Walid & Hammoudeh, Shawkat & Reboredo, Juan Carlos & Nguyen, Duc Khuong, 2014. "Do global factors impact BRICS stock markets? A quantile regression approach," Emerging Markets Review, Elsevier, vol. 19(C), pages 1-17.
    40. Liu, Jing & Ma, Feng & Yang, Ke & Zhang, Yaojie, 2018. "Forecasting the oil futures price volatility: Large jumps and small jumps," Energy Economics, Elsevier, vol. 72(C), pages 321-330.
    41. Wang, Yudong & Liu, Li & Wu, Chongfeng, 2017. "Forecasting the real prices of crude oil using forecast combinations over time-varying parameter models," Energy Economics, Elsevier, vol. 66(C), pages 337-348.
    42. Zhu, Xiaoneng & Zhu, Jie, 2013. "Predicting stock returns: A regime-switching combination approach and economic links," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4120-4133.
    43. repec:hal:journl:peer-00741630 is not listed on IDEAS
    44. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    45. Francis X. Diebold, 2015. "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 1-1, January.
    46. Barreto,Humberto & Howland,Frank, 2006. "Introductory Econometrics," Cambridge Books, Cambridge University Press, number 9780521843195.
    47. Wang, Gang-Jin & Xie, Chi & Lin, Min & Stanley, H. Eugene, 2017. "Stock market contagion during the global financial crisis: A multiscale approach," Finance Research Letters, Elsevier, vol. 22(C), pages 163-168.
    48. Weixian Wei, 2002. "Forecasting stock market volatility with non-linear GARCH models: a case for China," Applied Economics Letters, Taylor & Francis Journals, vol. 9(3), pages 163-166.
    49. Qi, Min & Wu, Yangru, 2003. "Nonlinear prediction of exchange rates with monetary fundamentals," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 623-640, December.
    50. Luo, Xingguo & Qin, Shihua, 2017. "Oil price uncertainty and Chinese stock returns: New evidence from the oil volatility index," Finance Research Letters, Elsevier, vol. 20(C), pages 29-34.
    51. Xiangjin B. Chen & Jiti Gao & Degui Li & Param Silvapulle, 2018. "Nonparametric Estimation and Forecasting for Time-Varying Coefficient Realized Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 88-100, January.
    52. Sévi, Benoît, 2014. "Forecasting the volatility of crude oil futures using intraday data," European Journal of Operational Research, Elsevier, vol. 235(3), pages 643-659.
    53. Gong, Xu & Lin, Boqiang, 2019. "Modeling stock market volatility using new HAR-type models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 194-211.
    54. Chen, Jian & Jiang, Fuwei & Li, Hongyi & Xu, Weidong, 2016. "Chinese stock market volatility and the role of U.S. economic variables," Pacific-Basin Finance Journal, Elsevier, vol. 39(C), pages 70-83.
    55. Wang Pu & Yixiang Chen & Feng Ma, 2016. "Forecasting the realized volatility in the Chinese stock market: further evidence," Applied Economics, Taylor & Francis Journals, vol. 48(33), pages 3116-3130, July.
    56. Ma, Feng & Li, Yu & Liu, Li & Zhang, Yaojie, 2018. "Are low-frequency data really uninformative? A forecasting combination perspective," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 92-108.
    57. Wang, Yudong & Ma, Feng & Wei, Yu & Wu, Chongfeng, 2016. "Forecasting realized volatility in a changing world: A dynamic model averaging approach," Journal of Banking & Finance, Elsevier, vol. 64(C), pages 136-149.
    58. He, Hongbo & Chen, Shou & Yao, Shujie & Ou, Jinghua, 2015. "Stock market interdependence between China and the world: A multi-factor R-squared approach," Finance Research Letters, Elsevier, vol. 13(C), pages 125-129.
    59. Zhang, Yaojie & Ma, Feng & Shi, Benshan & Huang, Dengshi, 2018. "Forecasting the prices of crude oil: An iterated combination approach," Energy Economics, Elsevier, vol. 70(C), pages 472-483.
    60. Douglas G. Santos & Flavio A. Ziegelmann, 2014. "Volatility Forecasting via MIDAS, HAR and their Combination: An Empirical Comparative Study for IBOVESPA," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(4), pages 284-299, July.
    61. Mark W. Watson & James H. Stock, 2004. "Combination forecasts of output growth in a seven-country data set," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 405-430.
    62. Fleming, Jeff & Kirby, Chris & Ostdiek, Barbara, 2003. "The economic value of volatility timing using "realized" volatility," Journal of Financial Economics, Elsevier, vol. 67(3), pages 473-509, March.
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    More about this item

    Keywords

    Volatility forecasting; Time-varying parameter; The Chinese stock market; Combination strategy; Global stock markets;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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