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Title: Regularised forecasting via smooth-rough partitioning of the regression coefficients Authors:  HyeYoung Maeng - London School of Economics (United Kingdom) [presenting]
Piotr Fryzlewicz - London School of Economics (United Kingdom)
Abstract: A way of modelling temporal dependence in random functions $X(t)$ in the framework of linear regression is introduced. Based on discretised curves ($X_i(t_0), X_i(t_1), ..., X_i(t_T)$), the final point $X_i(t_T)$ is predicted from ($X_i(t_0), X_i(t_1), ..., X_i(t_{T-1})$). 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 influential observations located close to $X_i(t_T)$, while the set of regression coefficients for the predictors positioned far from $X_i(t_T)$ are assumed to be sampled from a smooth function. This both regularises the prediction problem and reflects the `fading 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 two real data examples, involving country fertility and mortality data.