IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2309.01565.html
   My bibliography  Save this paper

Introducing the $\sigma$-Cell: Unifying GARCH, Stochastic Fluctuations and Evolving Mechanisms in RNN-based Volatility Forecasting

Author

Listed:
  • German Rodikov
  • Nino Antulov-Fantulin

Abstract

This paper introduces the $\sigma$-Cell, a novel Recurrent Neural Network (RNN) architecture for financial volatility modeling. Bridging traditional econometric approaches like GARCH with deep learning, the $\sigma$-Cell incorporates stochastic layers and time-varying parameters to capture dynamic volatility patterns. Our model serves as a generative network, approximating the conditional distribution of latent variables. We employ a log-likelihood-based loss function and a specialized activation function to enhance performance. Experimental results demonstrate superior forecasting accuracy compared to traditional GARCH and Stochastic Volatility models, making the next step in integrating domain knowledge with neural networks.

Suggested Citation

  • German Rodikov & Nino Antulov-Fantulin, 2023. "Introducing the $\sigma$-Cell: Unifying GARCH, Stochastic Fluctuations and Evolving Mechanisms in RNN-based Volatility Forecasting," Papers 2309.01565, arXiv.org.
  • Handle: RePEc:arx:papers:2309.01565
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2309.01565
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    4. Hu, Yan & Ni, Jian & Wen, Liu, 2020. "A hybrid deep learning approach by integrating LSTM-ANN networks with GARCH model for copper price volatility prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    5. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    6. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. Jacob A. Mincer, 1969. "Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance," NBER Books, National Bureau of Economic Research, Inc, number minc69-1, October.
    9. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201, Decembrie.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrea BUCCI, 2017. "Forecasting Realized Volatility A Review," Journal of Advanced Studies in Finance, ASERS Publishing, vol. 8(2), pages 94-138.
    2. Anders Eriksson & Daniel P. A. Preve & Jun Yu, 2019. "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model," JRFM, MDPI, vol. 12(3), pages 1-23, August.
    3. Xiangjin B. Chen & Jiti Gao & Degui Li & Param Silvapulle, 2013. "Nonparametric Estimation and Parametric Calibration of Time-Varying Coefficient Realized Volatility Models," Monash Econometrics and Business Statistics Working Papers 21/13, Monash University, Department of Econometrics and Business Statistics.
    4. Denisa Banulescu-Radu & Christophe Hurlin & Bertrand Candelon & Sébastien Laurent, 2016. "Do We Need High Frequency Data to Forecast Variances?," Annals of Economics and Statistics, GENES, issue 123-124, pages 135-174.
    5. Jonathan J. Reeves & Xuan Xie, 2014. "Forecasting stock return volatility at the quarterly frequency: an evaluation of time series approaches," Applied Financial Economics, Taylor & Francis Journals, vol. 24(5), pages 347-356, March.
    6. Janis Becker & Christian Leschinski, 2021. "Estimating the volatility of asset pricing factors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 269-278, March.
    7. Qiang Zhang & Rui Luo & Yaodong Yang & Yuanyuan Liu, 2018. "Benchmarking Deep Sequential Models on Volatility Predictions for Financial Time Series," Papers 1811.03711, arXiv.org.
    8. Xu, Buyun & Wu, Zhimin, 2025. "Real-time GARCH@CARR: A joint model of returns, realized measure of volatility and current intraday information," The North American Journal of Economics and Finance, Elsevier, vol. 76(C).
    9. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre.
    10. Michael McAleer & Marcelo C. Medeiros, 2009. "Forecasting Realized Volatility with Linear and Nonlinear Models," CARF F-Series CARF-F-189, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    11. Hui Qu & Ping Ji, 2016. "Modeling Realized Volatility Dynamics with a Genetic Algorithm," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(5), pages 434-444, August.
    12. Palandri, Alessandro, 2015. "Do negative and positive equity returns share the same volatility dynamics?," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 486-505.
    13. Bu, Ruijun & Hizmeri, Rodrigo & Izzeldin, Marwan & Murphy, Anthony & Tsionas, Mike, 2023. "The contribution of jump signs and activity to forecasting stock price volatility," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 144-164.
    14. Rui Luo & Weinan Zhang & Xiaojun Xu & Jun Wang, 2017. "A Neural Stochastic Volatility Model," Papers 1712.00504, arXiv.org, revised Dec 2018.
    15. Ke Yang & Langnan Chen & Fengping Tian, 2015. "Realized Volatility Forecast of Stock Index Under Structural Breaks," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(1), pages 57-82, January.
    16. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    17. Harry Vander Elst, 2015. "FloGARCH : Realizing long memory and asymmetries in returns volatility," Working Paper Research 280, National Bank of Belgium.
    18. Bonnier, Jean-Baptiste, 2022. "Forecasting crude oil volatility with exogenous predictors: As good as it GETS?," Energy Economics, Elsevier, vol. 111(C).
    19. F. Lilla, 2016. "High Frequency vs. Daily Resolution: the Economic Value of Forecasting Volatility Models," Working Papers wp1084, Dipartimento Scienze Economiche, Universita' di Bologna.
    20. Reschenhofer, Erhard & Mangat, Manveer Kaur & Stark, Thomas, 2020. "Volatility forecasts, proxies and loss functions," Journal of Empirical Finance, Elsevier, vol. 59(C), pages 133-153.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2309.01565. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.