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Energies2018,11, 1605 5.Conclusions Forecastingtimeseriesdataisconsideredasoneofthemostcriticalapplicationsandhasconcerned interestsofresearchers. Inthisstudy,wediscussedtheproblemofcombiningheterogeneousforecasters and showed that ensemble learningmethods couldbe readily adapted for thispurpose. Wehave introducedanovel theoretical ensemble framework integratingBPNN,SVR,andLR,basedon the principleofstacking;whichwasproposedfor theGOCforecasting. This frameworkhasbeenable to reduceuncertainty, improveforecastingperformance,andmanage thediversityof learningmodels in empiricalanalysis. Accordingto theexperimental resultsandanalyses, theproposedensemblemodelshavebeen abletooutperformtheclassicalensembleandsinglemodelsonOCdataanalyzedresults. Furthermore, all ensemblemodelshavebeenable toexceedthebestperforming individualmodelsonsingle-ahead, aswellas themulti-aheadhorizon. The advantages of proposed model to the knowledge comes therefore along three aspects as follows: Firstly, in methodology part, we have introduced a novel theoretical framework based on ensemble learningforOCforecasting.Althoughtheensembleconcept ismoredemandingregarding computationalrequirements, it cansignificantlyoutperformsinglemodelsandclassicalhybridmodels. While the idea is straightforward, it isyetarobustapproach,as it canoutperformlinearcombination methods,asonedoesnotknowaprioriwhichmodelwillperformbest. Secondly, theoreticallywehavedemonstrated thatensemblemethodscanbesuccessfullyused in thecontextofOCforecastingdueto theambiguitydecomposition. Thirdly,wehaveconductedaveryextensiveempiricalanalysisofadvancedmachine learning models, aswell as ensemblemethods. Just the calibrationaloneof suchawide rangeof ensemble models isveryrare in the literature, considering that the rankingof someevaluationmeasuresper model torun,whichwasnotonlydueto the limited. Thisstudyhas twolimitations including: theconsiderationof the integrationofheterogeneous algorithms (SVR, BPNNandLR)without using ensemble pruning for internal hyper-parameters; andtheevaluationprocess investigatedonsingledataset, so that thismodelcanverified indifferent datasets.All these limitationscouldbe interestingfutureresearch. Infuturework,homogeneousensemblemodelbasedSVRwithdifferentkernelscanbedeveloped andevaluated. Inaddition, investigatingensemblepruningbyusingevolutionaryalgorithmsthat provides an automatic optimization approach to SVRhyper-parameters, could be an interesting future research work in the hybrid-based energy forecasting field. Another direction of future work is toapplyensemblemodels inotherenergypredictionproblems, suchaspricing,production, andloadforecasting. AuthorContributions:M.A.K.performedtheexperiments,analyzedthedata, interpretedtheresultsandwrote thepaper. X.N.supervisedthiswork,allof theauthorswere involvedinpreparingthemanuscript. Funding:This researchreceivednoexternal funding. Acknowledgments:This researchwas fundedby theChineseScholarshipCouncil,China (underGrantsCSC No.2015-736012). Conflictsof Interest:Theauthorsdeclarenoconflictsof interest. References 1. Seni,G.;Elder, J.F.Ensemblemethods indatamining: Improvingaccuracythroughcombiningpredictions. InSynthesisLecturesonDataMiningandKnowledgeDiscovery; 2010;Volume2,pp.1–126. 2. Segal, M.R. Machine Learning Benchmarks and Random Forest Regression; Center for Bioinformatics and MolecularBiostatistics: SanFrancisco,CA,USA,2004. 3. Grömping, U. Variable importance assessment in regression: Linear regression versus random forest. Am.Stat. 2009,63, 308–319. [CrossRef] 284