By Hans-Martin Krolzig
This publication 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 well known for modelling non-linearities and regime shifts, quite often, in univariate eco nomic time sequence. This examine is meant to supply a scientific and operational ap proach to the econometric modelling of dynamic platforms topic to shifts in regime, in response to the Markov-switching vector autoregressive version. The examine provides a entire research of the theoretical homes of Markov-switching vector autoregressive tactics and the similar statistical equipment. The statistical techniques are illustrated with functions to empirical company cyde learn. This monograph is a revised model of my dissertation which has been permitted by way of the Economics division of the Humboldt-University of Berlin in 1996. It con sists normally of unpublished fabric which has been provided over the past years at meetings and in seminars. the main elements of this learn have been written whereas i used to be supported via 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 venture The Econometrics of Macroeconomic Forecasting based by way of the industrial and Social learn Council (ESRC) on the Institute of Economies and information, collage of Oxford. it's a excitement to checklist my due to those associations for his or her aid of my examine embodied during this study.
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Extra resources for Markov-Switching Vector Autoregressions: Modelling, Statistical Inference, and Application to Business Cycle Analysis
Thus, the desired conditional regime probabilities Pr(~tIY) can be derived by marginalization of Pr(~IY). In practice these cumbrous calculations can be simplified by a recursive algorithrn, a matter which is discussed in Chapter 5. The regime probabilities for future periods follow from the exogenous stochastic process of ~t, more precisely the Markov property of regimes, Pr(~T+hl~T, Y) = Pr(~T+hl~T ), L Pr(~T+hl~T, Y) Pr(~TIY) ~t L Pr(~T+hl~T) Pr(~TIY). 8). Forecasting MS-VAR processes is discussed in fulliength in Chapter 4.
An infinite number of regimes. lOModels where the regime is switching between deterministic and stochastic trends are considered by MCCULLOCH & TSAY [1994a]. A. A 27 Appendix: A Note on the Relation of SETAR to MS-AR Processes While the presumptions ofthe SETAR and the MS-AR model seem to be quite different, the relation between both model alternatives is rather dose. 19) is a par- ticular case 01 the Markov-switching model which is an MS/(2)-AR(O) model. L2)I(St-1 = 1)) cI> (r - /-L2 - (/-LI -:2)I(St-1 = 1») Pr(St = 1ISt-r}.
For example, a 'smooth' evolution of the parameters can be modeled by a time varying regression model, where the parameter vector ßt follows a Gaussian VAR process. This model can be presented by a linear normal state-space form which can be analyzed by the KaIman filter: Yt Xt(ß t - 13) + Ut F 1 (ß t - 13) + ... + F q(ßt+1-q - 13) + Vt, where Ut and Vt are Gaussian white noise. Ifthe Gaussian VAR(q) process is stable, we have the return to normality model proposed by ROSENBERG . 28) the time varying coefficients ßt fluctuate around their constant means ß.
Markov-Switching Vector Autoregressions: Modelling, Statistical Inference, and Application to Business Cycle Analysis by Hans-Martin Krolzig