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CPS1408 Caston S. et al.

























                                                    Figure 2

                  4.  Conclusion
                      Four models considered in this study were GAMs and AQR models with
                  and without interactions. The AQR model with pairwise interactions was found
                  to be the best fitting model. The forecasts from the four models were then
                  combined using an algorithm based on the pinball loss (convex combination
                  model) and also using quantile regression averaging (QRA). The AQR model
                  with interactions was then compared with the convex combination and QRA
                  models and the QRA model gave the most accurate forecasts. The QRA model
                  had the smallest prediction interval normalised average width and prediction
                  interval normalised average deviation.

                  References
                  1.  Bien, J.; Taylor, J.; Tibshirani, R. A lasso for hierarchical interactions. The
                     Annals of Statistics. 2013, 41(3), 1111-1141.
                     https://arxiv.org/ct?url=http3A2F2Fdx.doi. org2F10252E12142F13-
                     AOS1096&v=3d4226e4
                  2.  Bien, J.; Tibshirani, R. R package “hierNet”, version 1.6. 2015,
                     https://cran.r-project.org/ web/packages/hierNet/hierNet.pdf (Accessed
                     22 May 2017).
                  3.  Fasiolo, M.; Goude, Y.; Nedellec, R.; Wood, S.N. Fast calibrated additive
                     quantile regression. 2017. Available
                     online:https://github.com/mfasiolo/qgam/blob/master/draftqgam. pdf
                     (Accessed on 13 March 2017).
                  4.  Gaillard, P.; Goude, Y.; Nedellec, R. Additive models and robust
                     aggregation for GEFcom2014 probabilistic electric load and electricity




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