IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i8p1260-d1632745.html
   My bibliography  Save this article

Transformer-Based Downside Risk Forecasting: A Data-Driven Approach with Realized Downward Semi-Variance

Author

Listed:
  • Yuping Song

    (School of Finance and Business, Shanghai Normal University, Shanghai 200234, China
    These authors contributed equally to this work.)

  • Yuetong Zhang

    (School of Mathematics, Shandong University, Jinan 250100, China
    These authors contributed equally to this work.)

  • Po Ning

    (School of Finance and Business, Shanghai Normal University, Shanghai 200234, China
    These authors contributed equally to this work.)

  • Jiayi Peng

    (School of Finance and Business, Shanghai Normal University, Shanghai 200234, China)

  • Chunyu Kao

    (Securities Institute for Financial Studies, Shandong University, Jinan 250100, China)

  • Liang Hao

    (School of Finance and Business, Shanghai Normal University, Shanghai 200234, China)

Abstract

Realized downward semi-variance (RDS) has been realized as a key indicator to measure the downside risk of asset prices, and the accurate prediction of RDS can effectively guide traders’ investment behavior and avoid the impact of market fluctuations caused by price declines. In this paper, the RDS rolling prediction performance of the traditional econometric model, machine learning model, and deep learning model is discussed in combination with various relevant influencing factors, and the sensitivity analysis is further carried out with the rolling window length, prediction length, and a variety of evaluation methods. In addition, due to the characteristics of RDS, such as aggregation and jumping, this paper further discusses the robustness of the model under the impact of external events, the influence of emotional factors on the prediction accuracy of the model, and the results and analysis of the hybrid model. The empirical results show that (1) when the rolling window is set to 20, the overall prediction effect of the model in this paper is the best. Taking the Transformer model under SSE as an example, compared with the prediction results under the rolling window length of 5, 10, and 30, the RMSE improvement ratio reaches 24.69%, 15.90%, and 43.60%, respectively. (2) The multivariable Transformer model shows a better forecasting effect. Compared with traditional econometric, machine learning, and deep learning models, the average increase percentage of RMSE, MAE, MAPE, SMAPE, MBE, and SD indicators is 52.23%, 20.03%, 62.33%, 60.33%, 37.57%, and 18.70%, respectively. (3) In multi-step prediction scenarios, the DM test statistic of the Transformer model is significantly positive, and the prediction accuracy of the Transformer model remains stable as the number of prediction steps increases. (4) Under the impact of external events of COVID-19, the Transformer model has stability, and the addition of emotional factors can effectively improve the prediction accuracy. In addition, the model’s prediction performance and generalization ability can be further improved by stacked prediction models. An in-depth study of RDS forecasting is of great value to capture the characteristics of downside risks, enrich the financial risk measurement system, and better evaluate potential losses.

Suggested Citation

  • Yuping Song & Yuetong Zhang & Po Ning & Jiayi Peng & Chunyu Kao & Liang Hao, 2025. "Transformer-Based Downside Risk Forecasting: A Data-Driven Approach with Realized Downward Semi-Variance," Mathematics, MDPI, vol. 13(8), pages 1-28, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1260-:d:1632745
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/8/1260/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/8/1260/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chao Liang & Yu Wei & Likun Lei & Feng Ma, 2022. "Global equity market volatility forecasting: New evidence," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 594-609, January.
    2. 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.
    3. 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.
    4. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    5. Yilun Zhang & Yuping Song & Ying Peng & Hanchao Wang, 2024. "Volatility forecasting incorporating intraday positive and negative jumps based on deep learning model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(7), pages 2749-2765, November.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    8. Dongwoo Kim & Changryong Baek, 2020. "Factor-augmented HAR model improves realized volatility forecasting," Applied Economics Letters, Taylor & Francis Journals, vol. 27(12), pages 1002-1009, June.
    9. Dimos S. Kambouroudis & David G. McMillan & Katerina Tsakou, 2021. "Forecasting realized volatility: The role of implied volatility, leverage effect, overnight returns, and volatility of realized volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(10), pages 1618-1639, October.
    10. 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.
    11. Audrino, Francesco & Sigrist, Fabio & Ballinari, Daniele, 2020. "The impact of sentiment and attention measures on stock market volatility," International Journal of Forecasting, Elsevier, vol. 36(2), pages 334-357.
    12. Xingrui Jiao & Yuping Song & Yang Kong & Xiaolong Tang, 2022. "Volatility forecasting for crude oil based on text information and deep learning PSO‐LSTM model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(5), pages 933-944, August.
    13. Eunho Koo & Geonwoo Kim, 2023. "A New Neural Network Approach for Predicting the Volatility of Stock Market," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1665-1679, April.
    14. Chuong Luong & Nikolai Dokuchaev, 2018. "Forecasting of Realised Volatility with the Random Forests Algorithm," JRFM, MDPI, vol. 11(4), pages 1-15, October.
    15. repec:bla:jfinan:v:59:y:2004:i:3:p:1259-1294 is not listed on IDEAS
    16. Fang Jia & Boli Yang & Benjamin Miranda Tabak, 2021. "Forecasting Volatility of Stock Index: Deep Learning Model with Likelihood-Based Loss Function," Complexity, Hindawi, vol. 2021, pages 1-13, February.
    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. Gunnarsson, Elias Søvik & Isern, Håkon Ramon & Kaloudis, Aristidis & Risstad, Morten & Vigdel, Benjamin & Westgaard, Sjur, 2024. "Prediction of realized volatility and implied volatility indices using AI and machine learning: A review," International Review of Financial Analysis, Elsevier, vol. 93(C).
    2. Takuo Higashide & Katsuyuki Tanaka & Takuji Kinkyo & Shigeyuki Hamori, 2021. "New Dataset for Forecasting Realized Volatility: Is the Tokyo Stock Exchange Co-Location Dataset Helpful for Expansion of the Heterogeneous Autoregressive Model in the Japanese Stock Market?," JRFM, MDPI, vol. 14(5), pages 1-18, May.
    3. Izzeldin, Marwan & Muradoğlu, Yaz Gülnur & Pappas, Vasileios & Sivaprasad, Sheeja, 2021. "The impact of Covid-19 on G7 stock markets volatility: Evidence from a ST-HAR model," International Review of Financial Analysis, Elsevier, vol. 74(C).
    4. Chen, Wang & Lu, Xinjie & Wang, Jiqian, 2022. "Modeling and managing stock market volatility using MRS-MIDAS model," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 625-635.
    5. 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.
    6. 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.
    7. Zhu, Haibin & Bai, Lu & He, Lidan & Liu, Zhi, 2023. "Forecasting realized volatility with machine learning: Panel data perspective," Journal of Empirical Finance, Elsevier, vol. 73(C), pages 251-271.
    8. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2024. "Forecasting Daily Volatility of Stock Price Index Using Daily Returns and Realized Volatility," Econometrics and Statistics, Elsevier, vol. 32(C), pages 34-56.
    9. repec:uts:finphd:39 is not listed on IDEAS
    10. Liu, Chen & Wang, Chao & Tran, Minh-Ngoc & Kohn, Robert, 2025. "A long short-term memory enhanced realized conditional heteroskedasticity model," Economic Modelling, Elsevier, vol. 142(C).
    11. 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.
    12. 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.
    13. Aganin, Artem, 2017. "Forecast comparison of volatility models on Russian stock market," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 48, pages 63-84.
    14. Kuang, Wei, 2022. "The economic value of high-frequency data in equity-oil hedge," Energy, Elsevier, vol. 239(PA).
    15. 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.
    16. Naeem, Muhammad & Shahbaz, Muhammad & Saleem, Kashif & Mustafa, Faisal, 2019. "Risk analysis of high frequency precious metals returns by using long memory model," Resources Policy, Elsevier, vol. 61(C), pages 399-409.
    17. Alessandra Amendola & Vincenzo Candila & Antonio Naimoli & Giuseppe Storti, 2024. "Adaptive combinations of tail-risk forecasts," Papers 2406.06235, arXiv.org.
    18. Stefano Grassi & Nima Nonejad & Paolo Santucci De Magistris, 2017. "Forecasting With the Standardized Self‐Perturbed Kalman Filter," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 318-341, March.
    19. Asai, Manabu & McAleer, Michael & Medeiros, Marcelo C., 2012. "Modelling and forecasting noisy realized volatility," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 217-230, January.
    20. Yao Axel Ehouman, 2020. "Volatility transmission between oil prices and banks’ stock prices as a new source of instability: Lessons from the United States experience," Post-Print hal-02960571, HAL.
    21. 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.

    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:gam:jmathe:v:13:y:2025:i:8:p:1260-:d:1632745. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.