Cointegration_UW_Financial Data Modeling

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1、ComputationalFinanceandRiskManagementFinancialDataModelingandAnalysisinRGuyYollinAppliedMathematicsUniversityofWashingtonGuyYollin(Copyright©2013)FinancialDataModelingandAnalysisinRRegression1/67Outline1Spuriousregressionexample2Commontrendsandcointegration3Cointegrationexamples4

2、Testingforcointegration5ErrorcorrectionmodelsandtheJohansenmethod6TradingmodelsGuyYollin(Copyright©2013)FinancialDataModelingandAnalysisinRRegression2/67CointegrationreferencesPfaff,AnalysisofIntegratedandCointegratedTimeSerieswithR,2008Zivot,ModelingFinancialTimeSerieswithS-PLUS,

3、2005SDAFEchapter15GuyYollin(Copyright©2013)FinancialDataModelingandAnalysisinRRegression3/67Outline1Spuriousregressionexample2Commontrendsandcointegration3Cointegrationexamples4Testingforcointegration5ErrorcorrectionmodelsandtheJohansenmethod6TradingmodelsGuyYollin(Copyright©2013

4、)FinancialDataModelingandAnalysisinRRegression4/67SpuriousregressionRegressinganon-stationarytimeseriesonanothernon-stationarytimeseriesistypically†ameaninglessmodelcalledaspuriousregressionThespuriousregressionphenomenonisasfollows:coefficientestimatesconvergetoanon-normalrandomva

5、riablenotnecessarilycenteredonzerocoefficientt-stats:tβ→±∞asthesamplesizeT→∞DuetofalseassumptionthaterrorsareindependentR2→1asthesamplesizeT→∞AredflagforpossiblespuriousregressioniswhenR2>DW,theDurbin-Watsonstatistic‡‡"Spuriousregressionsineconometrics",JournalofEconometrics2,111-12

6、0.†ExceptinthecaseofcointegratedtimeseriesGuyYollin(Copyright©2013)FinancialDataModelingandAnalysisinRRegression5/67SpuriousregressionexampleRCode:Plotrandomtimeseries>set.seed(123456)>e1<-rnorm(500)>e2<-rnorm(500)>tt<-1:500>y1<-0.8*tt+cumsum(e1)>y2<-0.6*tt+cumsum(e2)>plot(as.ts(

7、cbind(y1,y2)),plot.type="single",col=c(2,4),ylab="y1,y2")400300y1,y220010000100200300400500TimeGuyYollin(Copyright©2013)FinancialDataModelingandAnalysisinRRegression6/67SpuriousregressionexampleRCode:Regressionanddiagnostics>lm.mod<-lm(y1~y2)>summary(lm.mod)Call:lm(formula=y1~y2)

8、Residuals:Min1QMedian3QMax-30.6541-11.52