IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v71y1999i1p24-41.html
   My bibliography  Save this article

Strongly Consistent Nonparametric Forecasting and Regression for Stationary Ergodic Sequences

Author

Listed:
  • Yakowitz, Sidney
  • Györfi, László
  • Kieffer, John
  • Morvai, Gusztáv

Abstract

Let {(Xi, Yi)} be a stationary ergodic time series with (X, Y) values in the product space Rd[circle times operator]R. This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and uniform distance) algorithm for inferring m(x)=E[Y0  X0=x] under the presumption that m(x) is uniformly Lipschitz continuous. Auto-regression, or forecasting, is an important special case, and as such our work extends the literature of nonparametric, nonlinear forecasting by circumventing customary mixing assumptions. The work is motivated by a time series model in stochastic finance and by perspectives of its contribution to the issues of universal time series estimation.

Suggested Citation

  • Yakowitz, Sidney & Györfi, László & Kieffer, John & Morvai, Gusztáv, 1999. "Strongly Consistent Nonparametric Forecasting and Regression for Stationary Ergodic Sequences," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 24-41, October.
    • Handle: RePEc:eee:jmvana:v:71:y:1999:i:1:p:24-41
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(99)91825-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Yakowitz, Sid, 1993. "Nearest neighbor regression estimation for null-recurrent Markov time series," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 311-318, November.
    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. Sancetta, A., 2005. "Forecasting Distributions with Experts Advice," Cambridge Working Papers in Economics 0517, Faculty of Economics, University of Cambridge.
    2. Didi Sultana & Louani Djamal, 2014. "Asymptotic results for the regression function estimate on continuous time stationary and ergodic data," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 1-22, June.
    3. Emmanuel Guerre, 2004. "Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series," Working Papers 2004-22, Center for Research in Economics and Statistics.

    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. Karlsen, Hans Arnfinn & Tjostheim, Dag, 1998. "Nonparametric estimation in null recurrent times series," SFB 373 Discussion Papers 1998,50, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Algoet, Paul & Györfi, László, 1999. "Strong Universal Pointwise Consistency of Some Regression Function Estimates," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 125-144, October.
    3. Arjen Hussem & Casper Ewijk & Harry Rele & Albert Wong, 2016. "The Ability to Pay for Long-Term Care in the Netherlands: A Life-cycle Perspective," De Economist, Springer, vol. 164(2), pages 209-234, June.
    4. Emmanuel Guerre, 2004. "Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series," Working Papers 2004-22, Center for Research in Economics and Statistics.
    5. Sancetta, Alessio, 2009. "Nearest neighbor conditional estimation for Harris recurrent Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2224-2236, November.
    6. E. Guerre & J. Maës, 1998. "Optimal Rate for Nonparametric Estimation in Deterministic Dynamical Systems," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 157-173, May.
    7. Arjen Hussem & Casper Ewijk & Harry Rele & Albert Wong, 2016. "The Ability to Pay for Long-Term Care in the Netherlands: A Life-cycle Perspective," De Economist, Springer, vol. 164(2), pages 209-234, June.
    8. Albert Wong & Hendriek Boshuizen & Johan Polder & José António Ferreira, 2017. "Assessing the inequality of lifetime healthcare expenditures: a nearest neighbour resampling approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 141-160, January.
    9. Guerre, Emmanuel, 2000. "Design Adaptive Nearest Neighbor Regression Estimation," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 219-244, November.

    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:eee:jmvana:v:71:y:1999:i:1:p:24-41. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.