IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/100878.html
   My bibliography  Save this paper

Regularised forecasting via smooth-rough partitioning of the regression coefficients

Author

Listed:
  • Maeng, Hye Young
  • Fryzlewicz, Piotr

Abstract

We introduce a way of modelling temporal dependence in random functions X(t) in the framework of linear regression. Based on discretised curves {Xi(t0),Xi(t1),…,Xi(tT)}, the final point Xi(tT) is predicted from {Xi(t0),Xi(t1),…,Xi(tT−1)}. The proposed model flexibly reflects the relative importance of predictors by partitioning the regression parameters into a smooth and a rough regime. Specifically, unconstrained (rough) regression parameters are used for observations located close to Xi(tT), while the set of regression coefficients for the predictors positioned far from Xi(tT) are assumed to be sampled from a smooth function. This both regularises the prediction problem and reflects the ‘decaying memory’ structure of the time series. The point at which the change in smoothness occurs is estimated from the data via a technique akin to change-point detection. The joint estimation procedure for the smoothness change-point and the regression parameters is presented, and the asymptotic behaviour of the estimated change-point is analysed. The usefulness of the new model is demonstrated through simulations and four real data examples, involving country fertility data, pollution data, stock volatility series and sunspot number data. Our methodology is implemented in the R package srp, available from CRAN.

Suggested Citation

  • Maeng, Hye Young & Fryzlewicz, Piotr, 2019. "Regularised forecasting via smooth-rough partitioning of the regression coefficients," LSE Research Online Documents on Economics 100878, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:100878
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/100878/
    File Function: Open access version.
    Download Restriction: no

    References listed on IDEAS

    as
    1. Hongxiao Zhu & Fang Yao & Hao Helen Zhang, 2014. "Structured functional additive regression in reproducing kernel Hilbert spaces," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 581-603, June.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    change-point detection; prediction; penalised spline; functional linear regression; EP/L014246/1;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    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:ehl:lserod:100878. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (LSERO Manager). General contact details of provider: http://edirc.repec.org/data/lsepsuk.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.