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Regularised forecasting via smooth-rough partitioning of the regression coefficients

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  • 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
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    File URL: http://eprints.lse.ac.uk/100878/
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    change-point detection; prediction; penalised spline; functional linear regression; EP/L014246/1;
    All these keywords.

    JEL classification:

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

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