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Same Error, Different Function: The Optimizer as an Implicit Prior in Financial Time Series

Author

Listed:
  • Federico Vittorio Cortesi
  • Giuseppe Iannone
  • Giulia Crippa
  • Tomaso Poggio
  • Pierfrancesco Beneventano

Abstract

Neural networks applied to financial time series operate in a regime of underspecification, where model predictors achieve indistinguishable out-of-sample error. Using large-scale volatility forecasting for S$\&$P 500 stocks, we show that different model-training-pipeline pairs with identical test loss learn qualitatively different functions. Across architectures, predictive accuracy remains unchanged, yet optimizer choice reshapes non-linear response profiles and temporal dependence differently. These divergences have material consequences for decisions: volatility-ranked portfolios trace a near-vertical Sharpe-turnover frontier, with nearly $3\times$ turnover dispersion at comparable Sharpe ratios. We conclude that in underspecified settings, optimization acts as a consequential source of inductive bias, thus model evaluation should extend beyond scalar loss to encompass functional and decision-level implications.

Suggested Citation

  • Federico Vittorio Cortesi & Giuseppe Iannone & Giulia Crippa & Tomaso Poggio & Pierfrancesco Beneventano, 2026. "Same Error, Different Function: The Optimizer as an Implicit Prior in Financial Time Series," Papers 2603.02620, arXiv.org.
    • Handle: RePEc:arx:papers:2603.02620
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    References listed on IDEAS

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    1. Luyang Chen & Markus Pelger & Jason Zhu, 2024. "Deep Learning in Asset Pricing," Management Science, INFORMS, vol. 70(2), pages 714-750, February.
    2. Rafael Reisenhofer & Xandro Bayer & Nikolaus Hautsch, 2022. "HARNet: A Convolutional Neural Network for Realized Volatility Forecasting," Papers 2205.07719, arXiv.org.
    3. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," Review of Finance, European Finance Association, vol. 33(5), pages 2223-2273.
    4. 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.
    5. James B. Heaton & Nicholas Polson & Jan H. Witte, 2017. "Rejoinder to ‘Deep learning for finance: deep portfolios’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(1), pages 19-21, January.
    6. Donaldson, R. Glen & Kamstra, Mark, 1997. "An artificial neural network-GARCH model for international stock return volatility," Journal of Empirical Finance, Elsevier, vol. 4(1), pages 17-46, January.
    7. Andrea Bucci, 2020. "Realized Volatility Forecasting with Neural Networks," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 502-531.
    8. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 4, pages 135-196, Elsevier.
    9. Capistrán, Carlos & Timmermann, Allan, 2009. "Forecast Combination With Entry and Exit of Experts," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 428-440.
    10. Branco, Rafael R. & Rubesam, Alexandre & Zevallos, Mauricio, 2024. "Forecasting realized volatility: Does anything beat linear models?," Journal of Empirical Finance, Elsevier, vol. 78(C).
    11. Gustavo Di-Giorgi & Rodrigo Salas & Rodrigo Avaria & Cristian Ubal & Harvey Rosas & Romina Torres, 2025. "Volatility forecasting using deep recurrent neural networks as GARCH models," Computational Statistics, Springer, vol. 40(6), pages 3229-3255, July.
    12. Wenfeng Ma & Yuxuan Hong & Yuping Song, 2024. "On Stock Volatility Forecasting under Mixed-Frequency Data Based on Hybrid RR-MIDAS and CNN-LSTM Models," Mathematics, MDPI, vol. 12(10), pages 1-21, May.
    13. D’Amato, Valeria & Levantesi, Susanna & Piscopo, Gabriella, 2022. "Deep learning in predicting cryptocurrency volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Radmir Mishelevich Leushuis & Nicolai Petkov, 2026. "Advances in forecasting realized volatility: a review of methodologies," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 12(1), pages 1-29, December.
    16. Vortelinos, Dimitrios I., 2017. "Forecasting realized volatility: HAR against Principal Components Combining, neural networks and GARCH," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 824-839.
    17. Chao Zhang & Yihuang Zhang & Mihai Cucuringu & Zhongmin Qian, 2022. "Volatility forecasting with machine learning and intraday commonality," Papers 2202.08962, arXiv.org, revised Feb 2023.
    18. J. B. Heaton & N. G. Polson & J. H. Witte, 2017. "Deep learning for finance: deep portfolios," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(1), pages 3-12, January.
    19. Souto Hugo Gobato & Moradi Amir, 2023. "Forecasting realized volatility through financial turbulence and neural networks," Economics and Business Review, Sciendo, vol. 9(2), pages 133-159, April.
    20. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2223-2273.
    21. 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.
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