Multi-step time series prediction intervals using neuroevolution

Multi-step time series forecasting (TSF) is a crucial element to support tactical decisions (e.g., designing production or marketing plans several months in advance). While most TSF research addresses only single-point prediction, prediction intervals (PIs) are useful to reduce uncertainty related to important decision making variables. In this paper, we explore a large set of neural network methods for multi-step TSF and that directly optimize PIs. This includes multi-step adaptations of recently proposed PI methods, such as lower--upper bound estimation (LUBET), its ensemble extension (LUBEXT), a multi-objective evolutionary algorithm LUBE (MLUBET) and a two-phase learning multi-objective evolutionary algorithm (M2LUBET). We also explore two new ensemble variants for the evolutionary approaches based on two PI coverage--width split methods (radial slices and clustering), leading to the MLUBEXT, M2LUBEXT, MLUBEXT2 and M2LUBEXT2 methods. A robust comparison was held by considering the rolling window procedure, nine time series from several real-world domains and with different characteristics, two PI quality measures (coverage error and width) and the Wilcoxon statistic. Overall, the best results were achieved by the M2LUBET neuroevolution method, which requires a reasonable computational effort for time series with a few hundreds of observations.This article is a result of the project NORTE-01- 0247-FEDER-017497, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (ERDF). We would also like to thank the anonymous reviewers for their helpful suggestionsinfo:eu-repo/semantics/publishedVersio

Polymerization of propene with modified constrained geometry complexes. Double-bond isomerization in pendant alkenyl groups attached to cyclopentadienyl ligands

Polymerization of propene with dimethylsilylene-bridged (amidocyclopentadienyl) dichlorotitanium( IV) complexes [TiCl2 {eta(5)-1-(t-BuSiMe2N-kappaN)- 2,3,4- Me-3 -5- R-C-5}], where R =Me (1), H (2), Ph (3), 4-fluorophenyl (4), but-2-en-2-yl (5), and butyl (6), combined with excess methylaluminoxane revealed a moderate effect of the substituent R on the catalyst activity and the molecular weight of polypropene. The asymmetric substitution in the position adjacent to the bridging carbon atom resulted in polymer yields decreasing in the order 1 > 6 > 3 approximate to 5 > 4 > 2 while polymers with the molecular weights (M-w) close to 2.5 x 10(5) for 1, 3, and 4, 1.5 x 10(5) for 5 and 6, and 7.5 x 10(4) for 2 were obtained. The C-13 NMR analysis of the polymers has shown that atactic polypropene is slightly enriched with syndiotactic triads for all the catalysts. Investigation of the crystal structure of 5 by X-ray crystallography revealed that the double bond in but-3-en-2-yl had shifted to an internal position to give the isomeric, but-2-en-2-yl-substituted complex. Likewise, the spectroscopic data for complex 7 prepared from the ligand containing but-3-en-1-yl substituent, indicate the absence of terminal double bond