Markov switching vector autoregressions: modelling, statistical inference, and application to business cycle analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1997
|
| Schriftenreihe: | Lecture notes in economics and mathematical systems
454 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 357 S. graph. Darst. |
| ISBN: | 3540630732 |
Internformat
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| 100 | 1 | |a Krolzig, Hans-Martin |d 1964- |e Verfasser |0 (DE-588)121703657 |4 aut | |
| 245 | 1 | 0 | |a Markov switching vector autoregressions |b modelling, statistical inference, and application to business cycle analysis |c Hans-Martin Krolzig |
| 246 | 1 | 3 | |a Markov-switching vector autoregressions |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
| 300 | |a XIV, 357 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in economics and mathematical systems |v 454 | |
| 502 | |a Zugl.: Berlin, Humboldt-Univ., Diss., 1996 | ||
| 650 | 7 | |a Business cycles |2 gtt | |
| 650 | 7 | |a Cycles économiques - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Estatistica aplicada a economia |2 larpcal | |
| 650 | 7 | |a Markov, Processus de |2 ram | |
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Sozialwissenschaften | |
| 650 | 4 | |a Business cycles -- Mathematical models | |
| 650 | 4 | |a Social sciences -- Statistical methods | |
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Datensatz im Suchindex
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| adam_text | Contents
Prologue 1
1 The Markov Switching Vector Autoregressive Model 6
1.1 General Introduction 6
1.2 Markov Switching Vector Autoregressions 10
1.2.1 The Vector Autoregression 10
1.2.2 ParticularMS VAR Processes 13
1.2.3 The Regime Shift Function 14
1.2.4 The Hidden Markov Chain 16
1.3 The Data Generating Process 17
1.4 Features of MS VAR Processes and Their Relation to Other Non¬
linear Models 20
1.4.1 Non Normality of the Distribution of the Observed Time
Series 21
1.4.2 Regime dependent Variances and Conditional Heteroske
dasticity 23
1.4.3 Regime dependent Autoregressive Parameters: ARCH and
Stochastic Unit Roots 24
1.5 Conclusion and Outlook 26
1.A Appendix: A Note on the Relation of SETAR to MS AR Processes 27
2 The State Space Representation 29
2.1 A Dynamic Linear State Space Representation for MS VAR Pro¬
cesses 30
2.1.1 The Gaussian Measurement Equation 32
2.1.2 The Non Normal VAR(1) Representation of the Hidden
Markov Chain 32
2.1.3 Linearity of the State Space Representation 33
x Contents
2.1.4 Markov Property of the State Space Representation 34
2.2 Specification of the State Space Representation 37
2.3 An Unrestricted State Space Representation 40
2.4 Prediction Error Decomposition and the Innovation State Space
Form 41
2.5 The MS VAR Model and Time Varying Coefficient Models 44
3 VARMA Representation of MSI VAR and MSM VAR Processes 47
3.1 Linearly Transformed Finite Order VAR Representations 48
3.2 VARMA Representation Theorems 53
3.2.1 VARMA Representation of Linearly Transformed Finite Or¬
der VAR Representations 53
3.2.2 ARMA Representation of a Hidden Markov Chain 54
3.2.3 VARMA Representations of MSI(M) VAR(0) Processes . 54
3.2.4 VARMA Representations of MSI(JW VAR(p) Processes . 55
3.2.5 VARMA Representations of MSM(M) VAR(p) Processes 56
3.3 The Autocovariance Function of MSI VAR and MSM VAR Pro¬
cesses 57
3.3.1 The ACF of the Regime Generating Process 58
3.3.2 The ACF of a Hidden Markov Chain Process 59
3.3.3 The ACF of MSM VAR Processes 60
3.3.4 The ACF of MSI VAR Processes 62
3.4 Outlook 64
4 Forecasting MS VAR Processes 65
4.1 MSPE Optimal Predictors 66
4.2 Forecasting MSM VAR Processes 68
4.3 Forecasting MSI VAR Processes 71
4.4 Forecasting MSA VAR Processes 72
4.5 Summary and Outlook 75
5 The BLHK Filter 77
5.1 Filtering 78
5.2 Smoothing 82
5.A Supplements 87
5.A.1 Conditional Moments of Regime 87
5.A.2 A Technical Remark on Hidden Markov Chains: The
MSI/MSIH(M) VAR(0) Model 88
Contents xi
6 Maximum Likelihood Estimation 89
6.1 The Likelihood Function 90
6.2 The Identification Problem 92
6.3 Normal Equations of the ML Estimator 95
6.3.1 Derivatives with Respect to the VAR Parameters 96
6.3.2 Derivatives with Respect to the Hidden Markov Chain Para¬
meters 97
6.3.3 Initial State 99
6.4 The EM Algorithm 101
6.4.1 Estimation of 7 103
6.4.2 Estimation of a under Homoskedasticity 107
6.4.3 Estimation of a under Heteroskedasticity 108
6.4.4 Convergence Criteria 109
6.5 Extensions and Alternatives 110
6.5.1 The Scoring Algorithm Ill
6.5.2 An Adaptive EM Algorithm (Recursive Maximum Likeli¬
hood Estimation) 113
6.5.3 Incorporating Bayesian Priors 115
6.5.4 Extension to General State Space Models with Markovian
Regime Shifts 116
6.6 Asymptotic Properties of the Maximum Likelihood Estimator 118
6.6.1 Asymptotic Normal Distribution of the ML Estimator .... 118
6.6.2 Estimation of the Asymptotic Variance Covariance Matrix 120
6.7 Conclusion 122
7 Model Selection and Model Checking 123
7.1 A Bottom up Strategy for the Specification of MS VAR Models .. 124
7.2 ARMA Representation Based Model Selection 129
7.3 Model Checking 131
7.3.1 Residual Based Model Checking 132
7.3.2 The Coefficient of Determination 133
7.4 Specification Testing 134
7.4.1 Likelihood Ratio Tests 135
7.4.2 Lagrange Multiplier Tests 135
7.4.3 Wald Tests 137
7.4.4 Newey Tauchen White Test for Dynamic Misspecification 139
7.5 Determination of the Number of Regimes 141
xii Contents
7.6 Some Critical Remarks 144
8 Multi Move Gibbs Sampling 145
8.1 Bayesian Analysis via the Gibbs Sampler 147
8.2 Bayesian Analysis of Linear Markov Switching Regression Models 149
8.3 Multi Move Gibbs Sampling of Regimes 152
8.3.1 Filtering and Smoothing Step 153
8.3.2 Stationary Probability Distribution and Initial Regimes ... 154
8.4 Parameter Estimation via Gibbs Sampling 155
8.4.1 Hidden Markov Chain Step 155
8.4.2 Inverted Wishart Step 157
8.4.3 Regression Step 159
8.5 Forecasting via Gibbs Sampling 163
8.6 Conclusions 165
9 Comparative Analysis of Parameter Estimation in Particular MS VAR
Models 167
9.1 Analysis of Regimes 169
9.2 Comparison of the Gibbs Sampler with the EM Algorithm 171
9.3 Estimation of VAR Parameters for Given Regimes 172
9.3.1 The Set of Regression Equations 172
9.3.2 Maximization Step of the EM Algorithm 174
9.3.3 Regression Step of the Gibbs Sampler 177
9.3.4 MSI Specifications 179
9.3.5 MSM Specifications 181
9.4 Summary 183
9.A Appendix: Tables 184
10 Extensions of the Basic MS VAR Model 199
10.1 Systems with Exogenous Variables 199
10.2 Distributed Lags in the Regime 202
10.2.1 The MSI(M,g) VAR(p) Model 202
10.2.2 VARMA Representations of MSI(M, g) VAR(p) Processes 203
10.2.3 Filtering and Smoothing 205
10.3 The Endogenous Markov Switching Vector Autoregressive Model 205
10.3.1 Models with Time Varying Transition Probabilities 205
10.3.2 Endogenous Selection 208
10.3.3 Filtering and Smoothing 209
Contents xiii
10.3.4 A Modified EM Algorithm 210
10.4 Summary and Outlook 211
11 Markov Switching Models of the German Business Cycle 213
11.1 MS AR Processes as Stochastic Business Cycle Models 216
11.2 Preliminary Analysis 217
11.2.1 Data 217
11.2.2 Traditional Turning Point Dating 219
11.2.3 ARMA Representation Based Model Pre Selection 220
11.3 The Hamilton Model 222
11.3.1 Estimation Results 222
11.3.2 Contribution to the Business Cycle Characterization 224
11.3.3 Impulse Response Analysis 227
11.3.4 Asymmetries of the Business Cycle 228
11.3.5 Kernel Density Estimation 229
11.4 Models with Markov Switching Intercepts 231
11.5 Regime Dependent and Conditional Heteroskedasticity 235
11.6 Markov Switching Models with Multiple Regimes 240
11.6.1 Outliers in a Three Regime Model 240
11.6.2 Outliers and the Business Cycle 242
11.6.3 A Hidden Markov Chain Model of the Business Cycle ... 243
11.6.4 A Highly Parameterized Model 245
11.6.5 Some Remarks on Testing 247
11.7 MS AR Models with Regime Dependent Autoregressive Parameters 247
11.8 An MSMH(3) AR(4) Business Cycle Model 250
11.9 Forecasting Performance 252
11.10 Conclusions 255
11 .A Appendix: Business Cycle Analysis with the Hodrick Prescott Filter 257
12 Markov Switching Models of Global and International Business
Cycles 259
12.1 Univariate Markov Switching Models 260
12.1.1 USA 263
12.1.2 Canada 264
12.1.3 United Kingdom 265
12.1.4 Germany 266
12.1.5 Japan 267
12.1.6 Australia 272
xiv Contents
12.1.7 Comparisons 274
12.2 Multi Country Growth Models with Markov Switching Regimes.. 277
12.2.1 Common Regime Shifts in the Joint Stochastic Process of
Economic Growth 277
12.2.2 Structural Breaks and the End of the Golden Age 278
12.2.3 Global Business Cycles 281
12.2.4 Rapid Growth Episodes and Recessions 284
12.3 Conclusions 288
12.A Appendix: Estimated MS DVAR Models 290
13 Cointegration Analysis of VAR Models with Markovian Shifts in Re¬
gime 297
13.1 Cointegrated VAR Processes with Markov Switching Regimes ... 298
13.1.1 Cointegration 298
13.1.2 TheMSCI VARModel 299
13.1.3 A State Space Representation for MSCI VAR Processes .. 302
13.2 A Cointegrated VARMA Representation for MSCI VAR Processes 306
13.3 A Two Stage Procedure 309
13.3.1 Cointegration Analysis 309
13.3.2 EM Algorithm 311
13.4 Global and International Business Cycles 312
13.4.1 VAR Order Selection 313
13.4.2 Cointegration Analysis 314
13.4.3 Granger Causality 316
13.4.4 Forecast Error Decomposition 318
13.5 Global Business Cycles in a Cointegrated System 320
13.6 Conclusions 323
13.A Appendix: Estimated CI VAR and MSCI VAR Models 325
Epilogue 329
References 331
Tables 347
Figures 35I
List of Notation 353
|
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| author | Krolzig, Hans-Martin 1964- |
| author_GND | (DE-588)121703657 |
| author_facet | Krolzig, Hans-Martin 1964- |
| author_role | aut |
| author_sort | Krolzig, Hans-Martin 1964- |
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| building | Verbundindex |
| bvnumber | BV011425809 |
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| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 338 - Production |
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| dewey-search | 338.5/42 338.5/42 21 |
| dewey-sort | 3338.5 242 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Thesis Book |
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| id | DE-604.BV011425809 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:09:32Z |
| institution | BVB |
| isbn | 3540630732 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007682876 |
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| physical | XIV, 357 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
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| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Krolzig, Hans-Martin 1964- Verfasser (DE-588)121703657 aut Markov switching vector autoregressions modelling, statistical inference, and application to business cycle analysis Hans-Martin Krolzig Markov-switching vector autoregressions Berlin [u.a.] Springer 1997 XIV, 357 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 454 Zugl.: Berlin, Humboldt-Univ., Diss., 1996 Business cycles gtt Cycles économiques - Modèles mathématiques ram Estatistica aplicada a economia larpcal Markov, Processus de ram Markov-modellen gtt Sciences sociales - Méthodes statistiques ram Tijdreeksen gtt Mathematisches Modell Sozialwissenschaften Business cycles -- Mathematical models Social sciences -- Statistical methods Vektor-autoregressives Modell (DE-588)4288533-4 gnd rswk-swf Konjunkturzyklus (DE-588)4032134-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Konjunkturzyklus (DE-588)4032134-4 s Vektor-autoregressives Modell (DE-588)4288533-4 s DE-604 Lecture notes in economics and mathematical systems 454 (DE-604)BV000000036 454 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007682876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krolzig, Hans-Martin 1964- Markov switching vector autoregressions modelling, statistical inference, and application to business cycle analysis Lecture notes in economics and mathematical systems Business cycles gtt Cycles économiques - Modèles mathématiques ram Estatistica aplicada a economia larpcal Markov, Processus de ram Markov-modellen gtt Sciences sociales - Méthodes statistiques ram Tijdreeksen gtt Mathematisches Modell Sozialwissenschaften Business cycles -- Mathematical models Social sciences -- Statistical methods Vektor-autoregressives Modell (DE-588)4288533-4 gnd Konjunkturzyklus (DE-588)4032134-4 gnd |
| subject_GND | (DE-588)4288533-4 (DE-588)4032134-4 (DE-588)4113937-9 |
| title | Markov switching vector autoregressions modelling, statistical inference, and application to business cycle analysis |
| title_alt | Markov-switching vector autoregressions |
| title_auth | Markov switching vector autoregressions modelling, statistical inference, and application to business cycle analysis |
| title_exact_search | Markov switching vector autoregressions modelling, statistical inference, and application to business cycle analysis |
| title_full | Markov switching vector autoregressions modelling, statistical inference, and application to business cycle analysis Hans-Martin Krolzig |
| title_fullStr | Markov switching vector autoregressions modelling, statistical inference, and application to business cycle analysis Hans-Martin Krolzig |
| title_full_unstemmed | Markov switching vector autoregressions modelling, statistical inference, and application to business cycle analysis Hans-Martin Krolzig |
| title_short | Markov switching vector autoregressions |
| title_sort | markov switching vector autoregressions modelling statistical inference and application to business cycle analysis |
| title_sub | modelling, statistical inference, and application to business cycle analysis |
| topic | Business cycles gtt Cycles économiques - Modèles mathématiques ram Estatistica aplicada a economia larpcal Markov, Processus de ram Markov-modellen gtt Sciences sociales - Méthodes statistiques ram Tijdreeksen gtt Mathematisches Modell Sozialwissenschaften Business cycles -- Mathematical models Social sciences -- Statistical methods Vektor-autoregressives Modell (DE-588)4288533-4 gnd Konjunkturzyklus (DE-588)4032134-4 gnd |
| topic_facet | Business cycles Cycles économiques - Modèles mathématiques Estatistica aplicada a economia Markov, Processus de Markov-modellen Sciences sociales - Méthodes statistiques Tijdreeksen Mathematisches Modell Sozialwissenschaften Business cycles -- Mathematical models Social sciences -- Statistical methods Vektor-autoregressives Modell Konjunkturzyklus Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007682876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
| work_keys_str_mv | AT krolzighansmartin markovswitchingvectorautoregressionsmodellingstatisticalinferenceandapplicationtobusinesscycleanalysis AT krolzighansmartin markovswitchingvectorautoregressions |