Markov-Switching Vector Autoregressions: Modelling, Statistical Inference, and Application to Business Cycle Analysis (Lecture Notes in Economics and Mathematical Systems (454))

This Book Contributes To Re Cent Developments On The Statistical Analysis Of Multiple Time Series In The Presence Of Regime Shifts. Markov-switching Models Have Become Popular For Modelling Non-linearities And Regime Shifts, Mainly, In Univariate Eco­ Nomic Time Series. This Study Is Intended To Provide A Systematic And Operational Ap­ Proach To The Econometric Modelling Of Dynamic Systems Subject To Shifts In Regime, Based On The Markov-switching Vector Autoregressive Model. The Study Presents A Comprehensive Analysis Of The Theoretical Properties Of Markov-switching Vector Autoregressive Processes And The Related Statistical Methods. The Statistical Concepts Are Illustrated With Applications To Empirical Business Cyde Research. This Monograph Is A Revised Version Of My Dissertation Which Has Been Accepted By The Economics Department Of The Humboldt-university Of Berlin In 1996. It Con­ Sists Mainly Of Unpublished Material Which Has Been Presented During The Last Years At Conferences And In Seminars. The Major Parts Of This Study Were Written While I Was Supported By The Deutsche Forschungsgemeinschajt (dfg), Berliner Graduier­ Tenkolleg Angewandte Mikroökonomik And Sondeiforschungsbereich 373 At The Free University And Humboldt-university Of Berlin. Work Was Finally Completed In The Project The Econometrics Of Macroeconomic Forecasting Founded By The Economic And Social Research Council (esrc) At The Institute Of Economies And Statistics, University Of Oxford. It Is A Pleasure To Record My Thanks To These Institutions For Their Support Of My Research Embodied In This Study. -- 1. The Markov-switching Vector Autoregressive Model -- 2. The State-space Representation -- 3. Varma-representation Of Msi-var And Msm-var Processes -- 4. Forecasting Ms-var Processes -- 5. The Blhk Filter -- 6. Maximum Likelihood Estimation -- 7. Model Selection And Model Checking -- 8. Multi-move Gibbs Sampling -- 8. Comparative Analysis Of Parameter Estimation In Particular Ms-var Models -- 10. Extensions Of The Basic Ms-var Model -- 11. Markov-switching Models Of The German Business Cycle -- 12. Markov-switching Models Of Global And International Business Cycles -- 13. Cointegration Analysis Of Var Models With Markovian Shifts In Regime. Hans-martin Krolzig. A Revised Version Of The Author's Dissertation, Accepted By The Economics Dept., Humboldt-university Of Berlin, 1996. Includes Bibliographical References (p. [331]-346). Front Matter....Pages i-xiv In the last decade time series econometrics has changed dramatically. One increasingly prominent field has become the treatment of regime shifts and non-linear mod- elling strategies. While the importance ofregime shifts, particularly in macroeconometric systems, seems to be generally accepted, there is no established theory suggesting a unique approach for specifying econometric models that embed changes in regime.....Pages 1-5 The Markov-Switching Vector Autoregressive Model....Pages 6-28 The State-Space Representation....Pages 29-46 VARMA-Representation of MSI-VAR and MSM-VAR Processes....Pages 47-64 Forecasting MS-VAR Processes....Pages 65-76 The BLHK Filter....Pages 77-88 Maximum Likelihood Estimation....Pages 89-122 Model Selection and Model Checking....Pages 123-144 Multi-Move Gibbs Sampling....Pages 145-166 Comparative Analysis of Parameter Estimation in Particular MS-VAR Models....Pages 167-198 Extensions of the Basic MS-VAR Model....Pages 199-211 Markov-Switching Models of the German Business Cycle....Pages 213-258 Markov-Switching Models of Global and International Business Cycles....Pages 259-296 Cointegration Analysis of VAR Models with Markovian Shifts in Regime....Pages 297-328 Epilogue....Pages 329-330 Back Matter....Pages 331-357 The book presents a systematic and operational approach to econometric modelling of time series subject to shifts in regime. The first part gives a comprehensive mathematical and statistical analysis of the Markov-switching vector autoregressive model. It deals with the theoretical properties and the statistical tools for empirical research. The discussed theoretical and practical developments will be of use to econometricians intending to construct and use models of dynamic, multivariate, possibly non-stationary systems. The second part includes an intensive study of international business cycles. Particular attention is paid to the case of Germany. It is designed so that it can be used by researchers who are interested in applying the methods without going into too much detail about the underlying theory