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A mixture deep neural network GARCH model for volatility forecasting

  • Received: 01 March 2023 Revised: 20 April 2023 Accepted: 22 April 2023 Published: 08 May 2023
  • Recently, deep neural networks have been widely used to solve financial risk modeling and forecasting challenges. Following this hotspot, this paper presents a mixture model for conditional volatility probability forecasting based on the deep autoregressive network and the Gaussian mixture model under the GARCH framework. An efficient algorithm for the model is developed. Both simulation and empirical results show that our model predicts conditional volatilities with smaller errors than the classical GARCH and ANN-GARCH models.

    Citation: Wenhui Feng, Yuan Li, Xingfa Zhang. A mixture deep neural network GARCH model for volatility forecasting[J]. Electronic Research Archive, 2023, 31(7): 3814-3831. doi: 10.3934/era.2023194

    Related Papers:

  • Recently, deep neural networks have been widely used to solve financial risk modeling and forecasting challenges. Following this hotspot, this paper presents a mixture model for conditional volatility probability forecasting based on the deep autoregressive network and the Gaussian mixture model under the GARCH framework. An efficient algorithm for the model is developed. Both simulation and empirical results show that our model predicts conditional volatilities with smaller errors than the classical GARCH and ANN-GARCH models.



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    [1] R. F. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50 (1982), 987–1007. https://doi.org/10.2307/1912773 doi: 10.2307/1912773
    [2] T. Bollerslev, Generalized autoregressive conditional heteroskedasticity, J. Econom., 31 (1986), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1 doi: 10.1016/0304-4076(86)90063-1
    [3] D. B. Nelson, Conditional heteroskedasticity in asset returns: A new approach, Econometrica, 59 (1991), 347–370. https://doi.org/10.2307/2938260 doi: 10.2307/2938260
    [4] L. R. Glosten, R. Jagannathan, D. E. Runkle, On the relation between the expected value and the volatility of the nominal excess return on stocks, J. Financ., 48 (1993), 1779–1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x doi: 10.1111/j.1540-6261.1993.tb05128.x
    [5] J. Hull, A. White, The pricing of options on assets with stochastic volatilities, J. Financ., 42 (1987), 281–300. https://doi.org/10.1111/j.1540-6261.1987.tb02568.x doi: 10.1111/j.1540-6261.1987.tb02568.x
    [6] B. J. Blair, S. H. Poon, S. J. Taylor, Forecasting S & P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns, in Handbook of Quantitative Finance and Risk Management, Springer, (2010), 1333–1344. https://doi.org/10.1007/978-0-387-77117-5
    [7] F. Audrino, D. Colangelo, Semi-parametric forecasts of the implied volatility surface using regression trees, Stat. Comput., 20 (2010), 421–434. https://doi.org/10.1007/s11222-009-9134-y doi: 10.1007/s11222-009-9134-y
    [8] C. Luong, N. Dokuchaev, Forecasting of realised volatility with the random forests algorithm, J. Risk Financial Manag., 11 (2018), 61. https://doi.org/10.3390/jrfm11040061 doi: 10.3390/jrfm11040061
    [9] S. Mittnik, N. Robinzonov, M. Spindler, Stock market volatility: identifying major drivers and the nature of their impact, J. Bank Financ., 58 (2015), 1–14. https://doi.org/10.1016/j.jbankfin.2015.04.003 doi: 10.1016/j.jbankfin.2015.04.003
    [10] Z. Li, B. Mo, H. Nie, Time and frequency dynamic connectedness between cryptocurrencies and financial assets in China, Int. Rev. Econ. Financ., 86 (2023), 46–57. http://dx.doi.org/10.1016/j.iref.2023.01.015 doi: 10.1016/j.iref.2023.01.015
    [11] Z. Li, H. Dong, C. Floros, A. Charemis, P. Failler, Re-examining bitcoin volatility: a CAViaR-based approach, Int. Rev. Econ. Financ., 58 (2022), 1320–1338. http://dx.doi.org/10.1080/1540496X.2021.1873127 doi: 10.1080/1540496X.2021.1873127
    [12] Z. Li, C. Yang, Z. Huang, How does the fintech sector react to signals from central bank digital currencies, Financ. Res. Lett., 50 (2022), 103308. http://dx.doi.org/10.1016/j.frl.2022.103308 doi: 10.1016/j.frl.2022.103308
    [13] Z. Li, L. Chen, H. Dong, What are bitcoin market reactions to its-related events, Int. Rev. Econ. Financ., 73 (2021), 1–10. http://dx.doi.org/10.1016/j.iref.2020.12.020 doi: 10.1016/j.iref.2020.12.020
    [14] T. Li, J. Wen, D. Zeng, K. Liu, Has enterprise digital transformation improved the efficiency of enterprise technological innovation? A case study on Chinese listed companies, Math. Biosci. Eng., 19 (2022), 12632–12654. http://dx.doi.org/10.3934/mbe.2022590 doi: 10.3934/mbe.2022590
    [15] Y. Liu, P. Failler, Z. Liu, Impact of environmental regulations on energy efficiency: a case study of China's air pollution prevention and control action plan, Sustainability, 14 (2022), 3168. http://dx.doi.org/10.3390/su14063168 doi: 10.3390/su14063168
    [16] Y. Liu, Z. Li, M. Xu, The influential factors of financial cycle spillover: evidence from China, Emerg. Mark. Financ. Tr., 56 (2020), 1336–1350. http://dx.doi.org/10.1080/1540496X.2019.1658076 doi: 10.1080/1540496X.2019.1658076
    [17] D. G. Kirikos, An evaluation of quantitative easing effectiveness based on out-of-sample forecasts, Natl. Account. Rev., 4 (2022), 378–389. https://dx.doi.org/10.3934/NAR.2022021 doi: 10.3934/NAR.2022021
    [18] J. Saleemi, COVID-19 and liquidity risk, exploring the relationship dynamics between liquidity cost and stock market returns, Natl. Account. Rev., 3 (2021), 218–236. https://dx.doi.org/10.3934/NAR.2021011 doi: 10.3934/NAR.2021011
    [19] S. A. Gyamerah, B. E. Owusu, E. K. Akwaa-Sekyi, Modelling the mean and volatility spillover between green bond market and renewable energy stock market, Green Finance, 4 (2022), 310–328. https://dx.doi.org/10.3934/GF.2022015 doi: 10.3934/GF.2022015
    [20] H. Siddiqi, Financial market disruption and investor awareness: the case of implied volatility skew, Quant. Finance Econ., 6 (2022), 505–517. https://dx.doi.org/10.3934/QFE.2022021 doi: 10.3934/QFE.2022021
    [21] L. Li, X. Zhang, Y. Li, C. Deng, Daily GARCH model estimation using high frequency data, J. Guangxi Norm. Univ., Nat. Sci., 39 (2021), 1181–1191.
    [22] S. A. Hamid, Z. Iqbal, Using neural networks for forecasting volatility of S & P 500 index futures prices, J. Bus. Res., 57 (2004), 1116–1125. https://doi.org/10.1016/S0148-2963(03)00043-2 doi: 10.1016/S0148-2963(03)00043-2
    [23] I. E. Livieris, E. Pintelas, P. Pintelas, A CNN-LSTM model for gold price time-series forecasting, Neural Comput. Appl., 32 (2020), 17351–17360. https://doi.org/10.1007/s00521-020-04867-x doi: 10.1007/s00521-020-04867-x
    [24] C. L. Dunis, X. Huang, Forecasting and trading currency volatility: an application of recurrent neural regression and model combination, J. Forecast., 21 (2002), 317–354. https://doi.org/10.1002/for.833 doi: 10.1002/for.833
    [25] R. G. Donaldson, M. Kamstra, An artificial neural network-GARCH model for international stock return volatility, J. Empir. Financ., 4 (1997), 17–46. https://doi.org/10.1016/S0927-5398(96)00011-4 doi: 10.1016/S0927-5398(96)00011-4
    [26] T. H. Roh, Forecasting the volatility of stock price index, Expert Syst. Appl., 33 (2007), 916–922. https://doi.org/10.1016/j.eswa.2006.08.001 doi: 10.1016/j.eswa.2006.08.001
    [27] M. Bildirici, Ö. Ö. Ersin, Improving forecasts of GARCH family models with the artificial neural networks:An application to the daily returns in Istanbul Stock Exchange, Expert Syst. Appl., 36 (2009), 7355–7362. https://doi.org/10.1016/j.eswa.2008.09.051 doi: 10.1016/j.eswa.2008.09.051
    [28] E. Hajizadeh, A. Seifi, M. H. F. Zarandi, I. B. Turksen, A hybrid modeling approach for forecasting the volatility of S & P 500 index return, Expert Syst. Appl., 39 (2012), 431–436. https://doi.org/10.1016/j.eswa.2011.07.033 doi: 10.1016/j.eswa.2011.07.033
    [29] W. Kristjanpoller, M. C. Minutolo, Gold price volatility: A forecasting approach using the Artificial Neural Network-GARCH model, Expert Syst. Appl., 42 (2015), 7245–7251. https://doi.org/10.1016/j.eswa.2015.04.058 doi: 10.1016/j.eswa.2015.04.058
    [30] N. Nikolaev, P. Tino, E. Smirnov, Time-dependent series variance learning with recurrent mixture density networks, Neurocomputing, 122 (2013), 501–512. https://doi.org/10.1016/j.neucom.2013.05.014 doi: 10.1016/j.neucom.2013.05.014
    [31] H. Y. Kim, C. H. Won, Forecasting the volatility of stock price index: A hybrid model integrating LSTM with multiple GARCH-type models, Expert Syst. Appl., 103 (2018), 25–37. https://doi.org/10.1016/j.eswa.2018.03.002 doi: 10.1016/j.eswa.2018.03.002
    [32] W. K. Liu, M. K. P. So, A GARCH model with artificial neural networks, Information, 11 (2020), 489. https://doi.org/10.3390/info11100489 doi: 10.3390/info11100489
    [33] D. Salinas, V. Flunkert, J. Gasthaus, T. Januschowski, DeepAR: Probabilistic forecasting with autoregressive recurrent networks, Int. J. Forecast., 36 (2020), 1181–1191. https://doi.org/10.1016/j.ijforecast.2019.07.001 doi: 10.1016/j.ijforecast.2019.07.001
    [34] P. Glasserman, D. Pirjol, W-shaped implied volatility curves and the Gaussian mixture model, Quant. Financ., 36 (2021), 1–21. https://doi.org/10.1080/14697688.2023.2165448 doi: 10.1080/14697688.2023.2165448
    [35] L. Scrucca, M. Fop, T. B. Murphy, A. E. Raftery, mclust 5: clustering, classification and density estimation using Gaussian finite mixture models, R J., 8 (2016), 289–317. https://doi.org/10.32614/RJ-2016-021 doi: 10.32614/RJ-2016-021
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