Multivariate Time Series Analysis: With R and Financial Applications

522 Pages·2013·5.49 MB·English

by  Ruey S. Tsay

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Multivariate Time Series Analysis
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Multivariate Time Series Analysis
With R and Financial Applications
RUEYS.TSAY
BoothSchoolofBusiness
UniversityofChicago
Chicago,IL
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Copyright(cid:2)c 2014byJohnWiley&Sons,Inc.Allrightsreserved
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LibraryofCongressCataloging-in-PublicationData:
Tsay,RueyS.,1951–
Multivariatetimeseriesanalysis:withRandfinancialapplications/RueyS.Tsay,BoothSchoolof
Business,UniversityofChicago,Chicago,IL.
pages cm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-61790-8(hardback)
1. Time-seriesanalysis. 2. R(Computerprogramlanguage) 3. Econometricmodels. I. Title.
QA280.T732014
519.5(cid:3)5–dc23
2014009453
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
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Tomyteacherandfriend
George
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Contents
Preface xv
Acknowledgements xvii
1 MultivariateLinearTimeSeries 1
1.1 Introduction, 1
1.2 SomeBasicConcepts, 5
1.2.1 Stationarity, 5
1.2.2 Linearity, 6
1.2.3 Invertibility, 7
1.3 Cross-CovarianceandCorrelationMatrices, 8
1.4 SampleCCM, 9
1.5 TestingZeroCross-Correlations, 12
1.6 Forecasting, 16
1.7 ModelRepresentations, 18
1.8 OutlineoftheBook, 22
1.9 Software, 23
Exercises, 23
2 StationaryVectorAutoregressiveTimeSeries 27
2.1 Introduction, 27
2.2 VAR(1)Models, 28
2.2.1 ModelStructureandGrangerCausality, 28
2.2.2 RelationtoTransferFunctionModel, 30
2.2.3 StationarityCondition, 31
2.2.4 Invertibility, 32
2.2.5 MomentEquations, 32
2.2.6 ImpliedModelsfortheComponents, 35
2.2.7 Moving-AverageRepresentation, 36
vii
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viii contents
2.3 VAR(2)Models, 37
2.3.1 StationarityCondition, 37
2.3.2 MomentEquations, 38
2.3.3 ImpliedMarginalComponentModels, 40
2.3.4 Moving-AverageRepresentation, 40
2.4 VAR(p)Models, 41
2.4.1 AVAR(1)Representation, 41
2.4.2 StationarityCondition, 42
2.4.3 MomentEquations, 42
2.4.4 ImpliedComponentModels, 43
2.4.5 Moving-AverageRepresentation, 43
2.5 Estimation, 44
2.5.1 Least-SquaresMethods, 44
2.5.2 MaximumLikelihoodEstimate, 47
2.5.3 LimitingPropertiesofLSEstimate, 49
2.5.4 BayesianEstimation, 55
2.6 OrderSelection, 61
2.6.1 SequentialLikelihoodRatioTests, 61
2.6.2 InformationCriteria, 63
2.7 ModelChecking, 66
2.7.1 ResidualCross-Correlations, 66
2.7.2 MultivariatePortmanteauStatistics, 71
2.7.3 ModelSimplification, 72
2.8 LinearConstraints, 80
2.9 Forecasting, 82
2.9.1 ForecastsofaGivenModel, 82
2.9.2 ForecastsofanEstimatedModel, 84
2.10 ImpulseResponseFunctions, 89
2.10.1 OrthogonalInnovations, 92
2.11 ForecastErrorVarianceDecomposition, 96
2.12 Proofs, 98
Exercises, 100
3 VectorAutoregressiveMoving-AverageTimeSeries 105
3.1 VectorMAModels, 106
3.1.1 VMA(1)Model, 106
3.1.2 PropertiesofVMA(q)Models, 110
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