Time Series for Macroeconomics and Finance.pdf

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1、TimeSeriesforMacroeconomicsandFinanceJohnH.Cochrane1GraduateSchoolofBusinessUniversityofChicago5807S.Woodlawn.ChicagoIL60637(773)702-3059john.cochrane@gsb.uchicago.eduSpring1997;PicturesaddedJan20051IthankGiorgioDeSantisformanyusefulcommentsonthismanuscri

2、pt.Copy-right°cJohnH.Cochrane1997,2005Contents1Preface72Whatisatimeseries?83ARMAmodels103.1Whitenoise............................103.2BasicARMAmodels.......................113.3Lagoperatorsandpolynomials.................113.3.1ManipulatingARMAswithlagoper

3、ators........123.3.2AR(1)toMA(∞)byrecursivesubstitution.......133.3.3AR(1)toMA(∞)withlagoperators...........133.3.4AR(p)toMA(∞),MA(q)toAR(∞),factoringlagpolynomials,andpartialfractions............143.3.5Summaryofallowedlagpolynomialmanipulations..163.4Mul

4、tivariateARMAmodels....................173.5ProblemsandTricks.......................194Theautocorrelationandautocovariancefunctions.214.1Definitions.............................214.2AutocovarianceandautocorrelationofARMAprocesses....224.2.1Summary.........

5、................2514.3Afundamentalrepresentation..................264.4Admissibleautocorrelationfunctions..............274.5Multivariateauto-andcrosscorrelations.............305PredictionandImpulse-ResponseFunctions315.1PredictingARMAmodels...............

6、.....325.2Statespacerepresentation....................345.2.1ARMAsinvectorAR(1)representation........355.2.2ForecastsfromvectorAR(1)representation.......355.2.3VARsinvectorAR(1)representation...........365.3Impulse-responsefunction....................375.

7、3.1Factsaboutimpulse-responses..............386StationarityandWoldrepresentation406.1Definitions.............................406.2ConditionsforstationaryARMA’s...............416.3WoldDecompositiontheorem..................436.3.1WhattheWoldtheoremdoesnotsay

8、..........456.4TheWoldMA(∞)asanotherfundamentalrepresentation...467VARs:orthogonalization,variancedecomposition,Grangercausality487.1OrthogonalizingVARs......................487.1.1Ambiguityofimpulse-responsefunctio