nonparametric time series prediction through adaptive model selection

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1、MachineLearning,39,5–34,2000.°c2000KluwerAcademicPublishers.PrintedinTheNetherlands.NonparametricTimeSeriesPredictionThroughAdaptiveModelSelection¤¤RONMEIR†rmeir@ee.technion.ac.ilDepartmentofElectricalEngineering,Technion,Haifa32000,IsraelEditor:LisaHellersteinAbstract.Weconsidertheprobl

2、emofone-stepaheadpredictionfortimeseriesgeneratedbyanunderlyingstationarystochasticprocessobeyingtheconditionofabsoluteregularity,describingthemixingnatureofprocess.Wemakeuseofrecentresultsfromthetheoryofempiricalprocesses,andadapttheuniformconvergenceframeworkofVapnikandChervonenkistoth

3、eproblemoftimeseriesprediction,obtainingfinitesamplebounds.Furthermore,byallowingboththemodelcomplexityandmemorysizetobeadaptivelydeterminedbythedata,wederivenonparametricratesofconvergencethroughanextensionofthemethodofstructuralriskminimizationsuggestedbyVapnik.Allourresultsarederivedfo

4、rgeneralLperrormeasures,andapplytobothexponentiallyandalgebraicallymixingprocesses.Keywords:timeseriesprediction,adaptivemodelselection,structuralriskminimization,mixingprocesses1.IntroductionTheproblemoftimeseriesmodelingandpredictionhasalonghistory,datingbacktothepioneeringworkofYulein

5、1927(Yule,1927).Mostoftheworksincethenuntilthe1970shasbeenconcernedwithparametricapproachestotheproblemwherebyasimple,usuallylinear,modelisfittedtothedata(forareviewofthisapproach,seeforexamplethetext-bookbyBrockwellandDavis(1991)).Whilemanyappealingmathematicalpropertiesoftheparametricap

6、proachhavebeenestablished,ithasbecomeclearovertheyearsthatthelimitationsoftheapproacharerathersevere,intheirimpositionofarigidstructureontheprocess.Oneofthemoreproductivesolutionstothisproblemhasbeentheextensionoftheclassicnonparametricmethodstothecaseoftimeseries(see,forexample,Gy¨orfiet

7、al.(1989)andBosq(1996)forareview).Inthisworkweusethetermparametricmodeltorefertoanymodelwhichimposesaspecificformontheestimatedfunction,whichisexactlyknownuptoafinitenumberofparameters.Nonparametricmodels,onthetheotherhand,donotimposeanystructuralassumptions,andcanmodelany(