Regularised forecasting via smooth-rough partitioning of the regression coefficients

Hye Young Maeng and Piotr Fryzlewicz

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: change-point detection; prediction; penalised spline; functional linear regression (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2019-06-22
New Economics Papers: this item is included in nep-for and nep-ore
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Published in Electronic Journal of Statistics, 22, June, 2019, 13(1), pp. 2093-2120. ISSN: 1935-7524

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