By Hans-Martin Krolzig
This e-book contributes to re cent advancements at the statistical research of a number of time sequence within the presence of regime shifts. Markov-switching types became renowned for modelling non-linearities and regime shifts, generally, in univariate eco nomic time sequence. This research is meant to supply a scientific and operational ap proach to the econometric modelling of dynamic structures topic to shifts in regime, according to the Markov-switching vector autoregressive version. The research provides a finished research of the theoretical houses of Markov-switching vector autoregressive techniques and the similar statistical equipment. The statistical recommendations are illustrated with functions to empirical company cyde examine. This monograph is a revised model of my dissertation which has been approved through the Economics division of the Humboldt-University of Berlin in 1996. It con sists regularly of unpublished fabric which has been offered over the last years at meetings and in seminars. the most important elements of this examine have been written whereas i used to be supported by way of the Deutsche Forschungsgemeinschajt (DFG), Berliner Graduier tenkolleg Angewandte Mikroökonomik and Sondeiforschungsbereich 373 on the loose college and Humboldt-University of Berlin. paintings used to be eventually accomplished within the undertaking The Econometrics of Macroeconomic Forecasting based via the commercial and Social study Council (ESRC) on the Institute of Economies and statistics, college of Oxford. it's a excitement to checklist my because of those associations for his or her aid of my examine embodied during this study.
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Additional info for Markov-Switching Vector Autoregressions: Modelling, Statistical Inference, and Application to Business Cycle Analysis
M are the regime-dependent parameter vectors. 5) is necessary to render the model identifiable (cf. 2). The assumption of a Gaussian error term Ut is chosen to make the model most operational. But even if the normality assumption is relaxed and substituted by any other probability distribution function, the procedures discussed here retain their justification as approximating techniques, for example as quasi-maximum likelihood estimations. 4. Indeed, the Markov chain governing the state vector ~t can be represented as a first-ordervector autoregression (cf.
4. ) the error ~t-l - €t-llt-l in the reconstruction of the regime vector at time t - 1. Analogously to et, the regime prediction error Ct can be considered as the innovation in the regime generating process given the information set Yt-l. 23) . The prediction-error-decomposition is now used in another specification of a statespace model, proposed by AOKI  and AOKI & HAVENNER , wh ich makes the relation between the state process and the innovations in the observed time series more apparent.
8). Forecasting MS-VAR processes is discussed in fulliength in Chapter 4. In this section we have given just a short introduction to some basic concepts related to MS-VAR models; the following chapters will provide broader analyses of the various topics. 4. 4 Features of MS-VAR Processes and Their Relation to Other Non-linear Models The Markov switching vector autoregressive model is a very general approach for modelling time series with changes in regime. In Chapter 3 it will be shown that MSVAR processes with shifting means or intercepts but regime-invariant variances and autoregressive parameters can be represented as non-normal linear state space models.