GARCH模型及其在金融中的应用PPT课件.ppt

ARCH GARCHModelswithApplicationinFinance 1 2 3 4 for 1 0and3 12 1 otherwisethekurtosisisnotfinite 5 ReturnsofShanghaiandShenzhenCompositeIndex 19Dec 1990through4Feb 2005 Daily SkewnessKurtosisSHCI5 979433140 400704SZCI0 92020615 824570 6 7 8 9 10 11 12 13 14 TheDataS PIndustrialsIndex Dailyfrom1stJan1990 29thSep20033586observationsintotal AProjectofGARCHonS PIndustrialsIndex 15 Objectives Procedures TheobjectiveofthisprojectistoestimatethevolatilityofSPost estimationanalysis 16 Pre estimationAnalysis TheobjectiveofthisprocedureistodeterminewhetherGARCHmodelsareappropriatefortheanalysisofthedataThefiguresdisplaythesampleACFofthereturnsbasedontheassumptionthatallautocorrelationsarezerobeyondlagzero ACFofsquaredreturnsshowsignificantcorrelationanddieoutslowly 17 Pre estimationAnalysis Ljung Box PierceQtestforautocorrelation at95 confidence Underthenullhypothesisofnoserialcorrelation theQ teststatisticisasymptoticallyChi Squaredistributed EngleArchtestforheteroscedasticity at95 confidence UnderthenullhypothesisthatatimeseriesisarandomsequenceofGaussiandisturbances i e noheteroscedasticity ThisteststatisticisalsoasymptoticallyChi Squaredistributed 18 2020 2 7 19 EstimationofParameters Themodel GARCH 1 1 ParametersestimatedbyGARCH 1 1 20 OutcomeofGARCH 1 1 Return EstimatedVolatility andInnovations i e residuals 21 Model Garch 1 1 Forecastvolatilityforthenext5days Standardisedresiduals UnconditionalStdof 22 Post estimationAnalysis Bothreturnsandresidualsshowvolatilityclustering ThesumofGARCHandARCHparametersiscloseto1 i etheprocessremainsstationary Standardisedresidualsshowsnoclustering nocorrelation andnoheteroscedasticity whichindicatesthemodelhassufficientexplanatorypowertowardthedata 23 FurtherDataAnalysis Lookingmorecarefullyatthedata itdoesn tseemtohavethenormaldistributionproperty whichGARCH 1 1 assumes 24 OutcomeofStudent tGARCH Model parameters estimatedvolatilty standardisedresiduals ACFofsquaredstandardisedresiduals testresults 25 TGARCH ThevolatilitymodelofTGARCH 26 Ljung Box PierceQtestforautocorrelation at95 confidence Underthenullhypothesisofnoserialcorrelation theQ teststatisticisasymptoticallyChi Squaredistributed Lag Teststatistics CriticalValue P value Testresults 10 5 6764 18 3070 0 8417 H0 15 20 2734 24 9958 0 1617 H0 20 25 5158 31 4104 0 1824 H0 EngleARCHtestforheteroscedasticity at95 confidence UnderthenullhypothesisthatatimeseriesisarandomsequenceofGaussiandisturbances i e noheteroscedasticity ThisteststatisticisalsoasymptoticallyChi Squaredistributed Lag Teststatistics CriticalValue P value Testresults 10 5 5887 18 3070 0 8486 H0 15 21 1278 24 9958 0 1328 H0 20 27 1601 31 4104 0 1308 H0 LBPQtest ARCHtest 27 OutcomeofTGARCH Return EstimatedVolatility andInnovations i e residuals 28 EGARCH Empiricalstudiesonfinancialserieshaveshownthattheyarecharacterisedbyincreasedconditionalvariancefollowingnegativeshocks badnews InEGARCHmodel thevolatilitydependsonthesignsoflaggedresidualsThedifferencebetweenabsoluteresidualsandexpectationoftheabsoluteresiduals Wedonothavetorestricttheparameterstobepositive 29 EGARCH ThevolatilitymodelofEGARCH 30 OutcomeofEGARCH Returns EstimatedVolatility andStandardisedresiduals 31 ARCH 20 Model ThemajorproblemwithARCHmodelisthatitrequireslonglag WeexperimentedwithARCH 1 andARCH 10 Bothmodelsfailtocapturethepropertyofserialcorrelationandheterscedasticityofthedata Forecastthevolatility