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1、Nonlinearcointegrationin?nancialtimeseriesClaudioPizziAbstract.Inthispaper,theconceptoflinearcointegrationasintroducedbyEngleandGranger[5]ismergedintothelocalparadigm.Adoptingalocalapproachenablestheachieve-mentofalocalerrorcorrectionmodelcharacterisedbydynamicpar
2、ameters.Anotherimportantresultobtainedusingthelocalparadigmisthatthemechanismthatleadsthedynamicsystembacktoasteadystateisnolongeraconstant:itisafunctionnotde?nedaprioributestimatedpointbypoint.Keywords:nonlinearity,cointegration,localpolynomialmodel1IntroductionO
3、neoftheaimsofthestatisticalanalysisofatimeseriesistoenabletheresearchertobuildasimpli?edrepresentationofthedata-generatingprocess(DGP)and/ortherelationshipamongstthedifferentphenomenaunderstudy.Themethodsforidenti-fyingandestimatingthesemodelsarebasedontheassumpti
4、onofthestationarityoftheDGP.Nevertheless,thisassumptionisoftenviolatedwhenconsidering?nancialphenomena,forexamplestockprice,interestrates,exchangeratesandsoon.The?nancialtimeseriesusuallypresentanon-stationarityofthe?rstorderifnothigher.Inthecaseoftheconstructiono
5、faregressivemodel,thepresenceofunitrootsinthetimeseriesmeansattentionshouldbepaidtothepossiblecointegrationamongstthevariables.Thecointegrationidea,whichcharacterisesthelong–runrelationshipbetweentwo(orseveral)timeseries,canberepresentedbyestimatingavectorofparame
6、tersandcanbeusedtobuildadynamicmodelthatenablesbothlong-runrelationshipsandalsosometransitionalshort-runinformationtobehighlighted.Thisenablestherepresentationofanerrorcorrectionmodelthatcanbeconsideredasadynamicsystemcharacterisedbythefactthatanydeparturefromthes
7、teadystategeneratesashort-rundynamic.ThelinearcointegrationconceptintroducedbyEngleandGranger[5]hasbeenbroadlydebatedintheliteratureandmuchhasbeenpublishedonthistopic.TheM.Corazzaetal.(eds.),MathematicalandStatisticalMethodsforActuarialSciencesandFinance?Springer-
8、VerlagItalia2010264ClaudioPizziresearchers’interesthasmainlybeentunedtotheproblemofestimatingthecointe-grationrelationship(itisworthmentioning,amongstot
