IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2010-39.html

Model Selection for Weakly Dependent Time Series Forecasting

Author

Listed:
  • Pierre Alquier

    (Crest)

  • Olivier Wintenberg

    (Crest)

Abstract

Observing a stationary time series, we propose a two-step procedure for the predictionof the next value of the time series. The first step follows machine learning theory paradigmand consists in determining a set of possible predictors as randomized estimators in (possiblynumerous) different predictive models. The second step follows the model selection paradigmand consists in choosing one predictor with good properties among all the predictors of the firststeps. We study our procedure for two different types of observations: causal Bernoulli shifts andbounded weakly dependent processes. In both cases, we give oracle inequalities: the risk of thechosen predictor is close to the best prediction risk in all predictive models that we consider. Weapply our procedure for predictive models such as linear predictors, neural networks predictorsand non-parametric autoregressive predictors.

Suggested Citation

  • Pierre Alquier & Olivier Wintenberg, 2010. "Model Selection for Weakly Dependent Time Series Forecasting," Working Papers 2010-39, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2010-39
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2010-39.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    2. Lacour, Claire, 2008. "Nonparametric estimation of the stationary density and the transition density of a Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 232-260, 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. Seok Young Hong & Oliver Linton, 2016. "Asymptotic properties of a Nadaraya-Watson type estimator for regression functions of in finite order," CeMMAP working papers 53/16, Institute for Fiscal Studies.
    2. Huaping Chen & Qi Li & Fukang Zhu, 2023. "A covariate-driven beta-binomial integer-valued GARCH model for bounded counts with an application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 805-826, October.
    3. Gaëlle Chagny & Claire Lacour, 2015. "Optimal adaptive estimation of the relative density," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 605-631, September.
    4. 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.
    5. Kengne, William, 2021. "Strongly consistent model selection for general causal time series," Statistics & Probability Letters, Elsevier, vol. 171(C).
    6. Aknouche, Abdelhakim & Demouche, Nacer, 2018. "Ergodicity conditions for a double mixed Poisson autoregression," MPRA Paper 88843, University Library of Munich, Germany.
    7. 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.
    8. Mengya Liu & Fukang Zhu & Ke Zhu, 2022. "Modeling normalcy‐dominant ordinal time series: An application to air quality level," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 460-478, May.
    9. 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.
    10. Sen, Shubhajit & Deb, Soudeep, 2026. "tSNE-Spec: A new classification method for multivariate time series data," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    11. Agosto, Arianna & Cavaliere, Giuseppe & Kristensen, Dennis & Rahbek, Anders, 2016. "Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 640-663.
    12. Paul Doukhan & Silika Prohl & Christian Robert, 2011. "Subsampling weakly dependent time series and application to extremes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 447-479, November.
    13. Paul Doukhan & Silika Prohl & Christian Robert, 2011. "Rejoinder on: Subsampling weakly dependent time series and application to extremes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 499-502, November.
    14. 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.
    15. Mamadou Lamine Diop & William Kengne, 2025. "Statistical learning for $$\psi $$ ψ -weakly dependent processes," Statistical Inference for Stochastic Processes, Springer, vol. 28(2), pages 1-23, August.
    16. Joseph Ngatchou-Wandji & Marwa Ltaifa, 2024. "A Cramér–von Mises test for a class of mean time dependent CHARN models with application to change-point detection," Statistical Inference for Stochastic Processes, Springer, vol. 27(1), pages 25-61, April.
    17. Comte, F. & Lacour, C. & Rozenholc, Y., 2010. "Adaptive estimation of the dynamics of a discrete time stochastic volatility model," Journal of Econometrics, Elsevier, vol. 154(1), pages 59-73, January.
    18. Weiß, Christian H. & Zhu, Fukang, 2024. "Conditional-mean multiplicative operator models for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    19. 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.
    20. Hong, Seok Young & Linton, Oliver, 2020. "Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff," Journal of Econometrics, Elsevier, vol. 219(2), pages 389-424.

    More about this item

    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:crs:wpaper:2010-39. 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: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    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.