IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v65y2024i3d10.1007_s00362-023-01442-z.html
   My bibliography  Save this article

Learning CHARME models with neural networks

Author

Listed:
  • José G. Gómez-García

    (AgroParisTech, INRAE, Université Paris-Saclay
    Normandie Université, UNICAEN)

  • Jalal Fadili

    (Normandie Université, CNRS, GREYC)

  • Christophe Chesneau

    (Normandie Université, UNICAEN)

Abstract

In this paper, we consider a model called CHARME (Conditional Heteroscedastic Autoregressive Mixture of Experts), a class of generalized mixture of nonlinear (non)parametric AR-ARCH time series. The main objective of this paper is to learn the autoregressive and volatility functions of this model with neural networks (NN). This approach is justified thanks to the universal approximation capacity of neural networks. On the other hand, in order to build the learning theory, it is necessary first to prove the ergodicity of the CHARME model. We therefore show in a general nonparametric framework that under certain Lipschitz-type conditions on the autoregressive and volatility functions, this model is stationary, ergodic and $$\tau $$ τ -weakly dependent. These conditions are much weaker than those in the existing literature. Moreover, this result forms the theoretical basis for deriving an asymptotic theory of the underlying parametric estimation, which we present for this model in a general parametric framework. Altogether, this allows to develop a learning theory for the NN-based autoregressive and volatility functions of the CHARME model, where strong consistency and asymptotic normality of the considered estimator of the NN weights and biases are guaranteed under weak conditions. Numerical experiments are reported to support our theoretical findings.

Suggested Citation

  • José G. Gómez-García & Jalal Fadili & Christophe Chesneau, 2024. "Learning CHARME models with neural networks," Statistical Papers, Springer, vol. 65(3), pages 1337-1374, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01442-z
    DOI: 10.1007/s00362-023-01442-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-023-01442-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-023-01442-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Lisa A. Korf & Roger J.-B. Wets, 2001. "Random LSC Functions: An Ergodic Theorem," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 421-445, May.
    3. Konstantinos Fokianos & Roland Fried, 2010. "Interventions in INGARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 210-225, May.
    4. Bolte, Jérôme & Castera, Camille & Pauwels, Edouard & Févotte, Cédric, 2019. "An Inertial Newton Algorithm for Deep Learning," TSE Working Papers 19-1043, Toulouse School of Economics (TSE).
    5. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    6. J. Dedecker & C. Prieur, 2004. "Coupling for τ-Dependent Sequences and Applications," Journal of Theoretical Probability, Springer, vol. 17(4), pages 861-885, October.
    7. Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1205-1225, December.
    8. Jean‐Pierre Stockis & Jürgen Franke & Joseph Tadjuidje Kamgaing, 2010. "On geometric ergodicity of CHARME models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 141-152, May.
    9. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
    10. Doukhan, Paul & Fokianos, Konstantinos & Li, Xiaoyin, 2012. "On weak dependence conditions: The case of discrete valued processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1941-1948.
    11. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    12. Claudia Kirch & Joseph Tadjuidje Kamgaing, 2012. "Testing for parameter stability in nonlinear autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 365-385, May.
    13. Karmakar, Sayar & Richter, Stefan & Wu, Wei Biao, 2022. "Simultaneous inference for time-varying models," Journal of Econometrics, Elsevier, vol. 227(2), pages 408-428.
    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. Huiyu Mao & Fukang Zhu & Yan Cui, 2020. "A generalized mixture integer-valued GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 527-552, September.
    2. William Kengne & Isidore S. Ngongo, 2022. "Inference for nonstationary time series of counts with application to change-point problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 801-835, August.
    3. Mawuli Segnon, 2022. "Strict stationarity of Poisson integer-valued ARCH processes of order infinity," CQE Working Papers 10222, Center for Quantitative Economics (CQE), University of Muenster.
    4. Vasiliki Christou & Konstantinos Fokianos, 2014. "Quasi-Likelihood Inference For Negative Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 55-78, January.
    5. Jiwon Kang & Sangyeol Lee, 2014. "Parameter Change Test for Poisson Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1136-1152, December.
    6. Hanan Elsaied & Roland Fried, 2014. "Robust Fitting Of Inarch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 517-535, November.
    7. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    8. Moysiadis, Theodoros & Fokianos, Konstantinos, 2014. "On binary and categorical time series models with feedback," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 209-228.
    9. Cui, Yunwei & Zheng, Qi, 2017. "Conditional maximum likelihood estimation for a class of observation-driven time series models for count data," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 193-201.
    10. Cui, Yunwei & Wu, Rongning, 2016. "On conditional maximum likelihood estimation for INGARCH(p,q) models," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 1-7.
    11. Aknouche, Abdelhakim & Bentarzi, Wissam & Demouche, Nacer, 2017. "On periodic ergodicity of a general periodic mixed Poisson autoregression," MPRA Paper 79650, University Library of Munich, Germany.
    12. Mengya Liu & Qi Li & Fukang Zhu, 2020. "Self-excited hysteretic negative binomial autoregression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 385-415, September.
    13. Kang, Jiwon & Lee, Sangyeol, 2014. "Minimum density power divergence estimator for Poisson autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 44-56.
    14. Mamadou Lamine Diop & William Kengne, 2017. "Testing Parameter Change in General Integer-Valued Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 880-894, November.
    15. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
    16. Youngmi Lee & Sangyeol Lee, 2019. "CUSUM test for general nonlinear integer-valued GARCH models: comparison study," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1033-1057, October.
    17. Yan Cui & Fukang Zhu, 2018. "A new bivariate integer-valued GARCH model allowing for negative cross-correlation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 428-452, June.
    18. Aknouche, Abdelhakim & Bendjeddou, Sara, 2016. "Negative binomial quasi-likelihood inference for general integer-valued time series models," MPRA Paper 76574, University Library of Munich, Germany, revised 03 Feb 2017.
    19. Youngmi Lee & Sangyeol Lee & Dag Tjøstheim, 2018. "Asymptotic normality and parameter change test for bivariate Poisson INGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 52-69, March.
    20. Dag Tjøstheim, 2012. "Rejoinder on: Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 469-476, September.

    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:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01442-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.