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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
    1. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    2. Müller, Hans-Georg & Sen, Rituparna & Stadtmüller, Ulrich, 2011. "Functional data analysis for volatility," Journal of Econometrics, Elsevier, vol. 165(2), pages 233-245.
    3. Aldo Goia & Philippe Vieu, 2015. "A partitioned Single Functional Index Model," Computational Statistics, Springer, vol. 30(3), pages 673-692, September.
    4. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
    5. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    6. Lajos Horváth & Piotr Kokoszka & Ron Reeder, 2013. "Estimation of the mean of functional time series and a two-sample problem," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(1), pages 103-122, January.
    7. Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2010. "Tests for Error Correlation in the Functional Linear Model," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1113-1125.
    8. 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.
    9. Alexander Aue & Diogo Dubart Norinho & Siegfried Hörmann, 2015. "On the Prediction of Stationary Functional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 378-392, March.
    10. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    11. Goia, Aldo, 2012. "A functional linear model for time series prediction with exogenous variables," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1005-1011.
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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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