IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2410.11113.html
   My bibliography  Save this paper

Statistical Properties of Deep Neural Networks with Dependent Data

Author

Listed:
  • Chad Brown

Abstract

This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNN estimators are given. The first establishes rates for convergence in probability under nonstationary data. The second provides non-asymptotic probability bounds on $\mathcal{L}^{2}$-errors under stationary $\beta$-mixing data. I apply these results to DNN estimators in both regression and classification contexts imposing only a standard H\"older smoothness assumption. The DNN architectures considered are common in applications, featuring fully connected feedforward networks with any continuous piecewise linear activation function, unbounded weights, and a width and depth that grows with sample size. The framework provided also offers potential for research into other DNN architectures and time-series applications.

Suggested Citation

  • Chad Brown, 2024. "Statistical Properties of Deep Neural Networks with Dependent Data," Papers 2410.11113, arXiv.org, revised Nov 2024.
  • Handle: RePEc:arx:papers:2410.11113
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2410.11113
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Maxwell B. Stinchcombe & Halbert White, 1992. "Some Measurability Results for Extrema of Random Functions Over Random Sets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 495-514.
    2. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. 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.
    5. 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.
    6. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    7. Qizhao Chen & Vasilis Syrgkanis & Morgane Austern, 2022. "Debiased Machine Learning without Sample-Splitting for Stable Estimators," Papers 2206.01825, arXiv.org, revised Nov 2022.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chad Brown, 2024. "Inference in Partially Linear Models under Dependent Data with Deep Neural Networks," Papers 2410.22574, arXiv.org.

    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. Gomez-Gonzalez, Jose E. & Uribe, Jorge M. & Valencia, Oscar, 2024. "Sovereign Risk and Economic Complexity," IDB Publications (Working Papers) 13393, Inter-American Development Bank.
    2. Philippe Goulet Coulombe & Maximilian Gobel, 2023. "Maximally Machine-Learnable Portfolios," Working Papers 23-01, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management, revised Apr 2023.
    3. Chad Brown, 2024. "Inference in Partially Linear Models under Dependent Data with Deep Neural Networks," Papers 2410.22574, arXiv.org.
    4. Casas Villalba, Maria Isabel, 2020. "Adaptative predictability of stock market returns," DES - Working Papers. Statistics and Econometrics. WS 31648, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Michalski, Lachlan & Low, Rand Kwong Yew, 2024. "Determinants of corporate credit ratings: Does ESG matter?," International Review of Financial Analysis, Elsevier, vol. 94(C).
    6. Andrii Babii & Ryan T. Ball & Eric Ghysels & Jonas Striaukas, 2024. "Panel data nowcasting: The case of price–earnings ratios," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(2), pages 292-307, March.
    7. Kirill Borusyak & Peter Hull & Xavier Jaravel, 2023. "Design-Based Identification with Formula Instruments: A Review," NBER Working Papers 31393, National Bureau of Economic Research, Inc.
    8. Bakalli, Gaetan & Guerrier, Stéphane & Scaillet, Olivier, 2023. "A penalized two-pass regression to predict stock returns with time-varying risk premia," Journal of Econometrics, Elsevier, vol. 237(2).
    9. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    10. Wang, Yudong & Hao, Xianfeng, 2022. "Forecasting the real prices of crude oil: A robust weighted least squares approach," Energy Economics, Elsevier, vol. 116(C).
    11. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    12. Tobias Götze & Marc Gürtler & Eileen Witowski, 2020. "Improving CAT bond pricing models via machine learning," Journal of Asset Management, Palgrave Macmillan, vol. 21(5), pages 428-446, September.
    13. Wen, Danyan & Liu, Li & Wang, Yudong & Zhang, Yaojie, 2022. "Forecasting crude oil market returns: Enhanced moving average technical indicators," Resources Policy, Elsevier, vol. 76(C).
    14. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    15. Malakhov, Alexey & Riley, Timothy B. & Yan, Qing, 2024. "Do hedge funds bet against beta?," International Review of Economics & Finance, Elsevier, vol. 93(PA), pages 1507-1525.
    16. 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.
    17. Eghbal Rahimikia & Stefan Zohren & Ser-Huang Poon, 2021. "Realised Volatility Forecasting: Machine Learning via Financial Word Embedding," Papers 2108.00480, arXiv.org, revised Nov 2024.
    18. Daníelsson, Jón & Macrae, Robert & Uthemann, Andreas, 2022. "Artificial intelligence and systemic risk," Journal of Banking & Finance, Elsevier, vol. 140(C).
    19. Guo, Li & Sang, Bo & Tu, Jun & Wang, Yu, 2024. "Cross-cryptocurrency return predictability," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    20. Rad, Hossein & Low, Rand Kwong Yew & Miffre, Joëlle & Faff, Robert, 2023. "The commodity risk premium and neural networks," Journal of Empirical Finance, Elsevier, vol. 74(C).

    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:2410.11113. 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.