Estima所制作的有关VAR模型在RATS9.0上面实现的手册，是Edition 2.0版本的手册(最新版)，具体目录如下                                                                                                                                                [size=12.000000pt]

1 Introduction 1

.     1.1 VectorAutoregressions...................... 1 


.     1.2 LogLikelihoodFunction ..................... 2 


.     1.3 ChoosingLagLength....................... 3 


.     1.4  SYSTEMdefinitionandESTIMATE................6 


.     1.5 VariablesandResiduals...................... 8 


.     1.6 AlternativeEstimationMethods.................. 9 


.     1.1 LagSelectionbyAIC .......................... 11 1.2 EstimationTechniques.........................12 1.3 LongLagVAR..............................13 


2 Impulse Response Functions 14

.     2.1 MovingAverageRepresentation.................. 14 


.     2.2 ComputingImpulseResponses .................. 16 


.     2.3 Orthogonalization . . . . . . . . . . . . . . . . . . . . . . . . 21 


.     2.4 VarianceDecomposition...................... 23 


.     2.5 RATSTipsandTricks ...................... 26 
2.1 IRFwithinputshocks......................... 28 2.2 IRFwithCholeskishocks....................... 29 


3 Error Bands 30

.     3.1 Deltamethod .......................... 30 


.     3.2 Bootstrapping.......................... 33 3.2.1Kilianbootstrap-after-bootstrap. . . . . . . . . . . . . . . . 34 


.     3.3 MonteCarloIntegration ..................... 35 3.3.1 Creating%%RESPONSES...................38 3.3.2 The@MCPROCESSIRFprocedure.............. 39 


3.4RATSTipsandTricks ...................... 42 3.4.1The%MODELfunctionfamily.................. 42 3.4.2 BlockSampling......................... 43

.     3.1  ErrorBandsbyDeltaMethod ..................... 45 


.     3.2  ErrorBandsbyBootstrapping..................... 46 


.     3.3  ErrorBandsbyKilianbootstrap ................... 47 


.     3.4  ErrorBandsbyMonteCarlo...................... 48 


.     3.5  Error Bands by Bootstrapping with Random Initial Values .. . . 49 


4 Historical Decomposition and Counterfactual Simulations 51

.     4.1 HistoricalDecomposition..................... 51 


.     4.2 CounterfactualSimulations.................... 53 


.     4.3 ErrorBands........................... 54 
4.1 HistoricalDecomposition........................54 


5 Structural VAR’s 56

.     5.1 EigenFactorizations....................... 56 


.     5.2 GeneralizedImpulseResponses.................. 57 


.     5.3 ParametricStructuralVAR’s ................... 58 


.     5.4 Identification........................... 61 


.     5.5  Estimation............................62 


.     5.6 StructuralResiduals....................... 67 


.     5.7 ErrorBands........................... 67

.                      5.7.1  Bootstrapping.......................... 68 


.                      5.7.2  Monte Carlo: Deriving the PosteriorDistribution . . . . . 68 


.                      5.7.3  MonteCarlowithImportanceSampling . . .. . . . . . . . 71 


.                      5.7.4  Monte Carlo with Random Walk Metropolis. . . . . . . . . 76 


.                      5.7.5  Monte Carlo with the Waggoner-ZhaSampler . . . . . . . 81 


.     5.8 TipsandTricks ......................... 84 5.8.1 UsingPARMSETS........................ 84 5.8.2 Waggoner-Zhasampler..................... 85

.                      5.1  Eigenfactorization........................... 87 


.                      5.2  SVAR:A-styleModel.......................... 88 


Contents iii

5.3 SVAR:A-Bstylemodel ......................... 90 5.4 SVAR:ImportanceSamplingforErrorBands. . . . . . . . . . . . 92 5.5 SVAR:RandomWalkMetropolisforErrorBands.. . . . . . . . . 96 5.6 SVAR:Waggoner-ZhaSampler.................... 99

6 Semi-Structural VAR’s 101

.     6.1 ForcedFactorProcedure......................102 


.     6.2 Short-andLong-RunRestrictions.................103 


.     6.3 Multi-stepRestrictions......................105 


.     6.4 ErrorBands...........................107 
6.1 Blanchard-QuahDecomposition....................110 6.2 Multi-StepRestrictions.........................112 6.3 Short- and Long-RunRestrictions with Error Bands . . . . . . . . 114 


7 Sign Restrictions 116

.     7.1 GeneratingImpulseVectors....................116 


.     7.2 Penaltyfunctions.........................122 


.     7.3 MultipleShocks.........................124 
7.3.1 FORCEDFACTOR and the QR Decomposition . . . .. . . 125 


.     7.4 ZeroConstraints.........................126 


.     7.5  Fry-PaganCritique........................127


.     7.6 HistoricalDecomposition.....................130 


.     7.7 Convenience functions for sign restrictions . . . . . . . . . . . . . 131
7.1 SignRestrictions:PartI ........................ 134 7.2 SignRestrictions:PartII........................136 7.3 SignRestrictions:PartIII....................... 139 7.4 SignRestrictions:MedianTargetMethod. . . . . . . . . . . . . . 141 


A Probability Distributions 145

.     A.1 Multivariate Normal . . . . . . . . . . . . . . . . . . . . . . . 145 


.     A.2  WishartDistribution . . . . . . . . . . . . . . . . . . . . . . . 146 


.     A.3 GammaDistribution . . . . . . . . . . . . . . . . . . . . . . . 147 


.     A.4 InverseGammaDistribution . . . . . . . . . . . . . . . . . . . 148 


Contents iv

.     B  VAR Likelihood Function 149 


.     C  Properties of Multivariate Normals 152 


.     D  Deriving the Schwarz criterion 155 


.     E  Delta method 157 


.     F  Gibbs Sampling and Markov Chain Monte Carlo 158 


Bibliography 162 Index 164

除了手册原文，还附上与手册中有关的例子code和data