nonlinear cointegration in financial time series

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1、NonlinearcointegrationinfinancialtimeseriesClaudioPizziAbstract.Inthispaper,theconceptoflinearcointegrationasintroducedbyEngleandGranger[5]ismergedintothelocalparadigm.Adoptingalocalapproachenablestheachieve-mentofalocalerrorcorrectionmodelcharacterisedbydynamicpar

2、ameters.Anotherimportantresultobtainedusingthelocalparadigmisthatthemechanismthatleadsthedynamicsystembacktoasteadystateisnolongeraconstant:itisafunctionnotdefinedaprioributestimatedpointbypoint.Keywords:nonlinearity,cointegration,localpolynomialmodel1IntroductionO

3、neoftheaimsofthestatisticalanalysisofatimeseriesistoenabletheresearchertobuildasimplifiedrepresentationofthedata-generatingprocess(DGP)and/ortherelationshipamongstthedifferentphenomenaunderstudy.Themethodsforidenti-fyingandestimatingthesemodelsarebasedontheassumpti

4、onofthestationarityoftheDGP.Nevertheless,thisassumptionisoftenviolatedwhenconsideringfinancialphenomena,forexamplestockprice,interestrates,exchangeratesandsoon.Thefinancialtimeseriesusuallypresentanon-stationarityofthefirstorderifnothigher.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