Abstract
The previous chapter introduced the state-space representation as the basic tool for describing vector autoregressive processes with Markovian regime shifts. This chapter looks in greater depth at the relationship between Markov-switching vector autoregressions and linear time series models. We develop a finite order VARMA representations theorem for vector autoregressive processes with Markovian regime shifts in the mean or the intercept term of the multiple time series. This result generalizes concepts recently proposed by Poskitt & Chung [1994] for univariate hidden Markov-chains, and by Krolzig [1995] for univariate MSM(M)-AR(p) and MSI(M)-AR(p) processes.
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While the hidden Markov-chain model is not widely used in econometrics, it has received considerable attention in engineering, see e.g. Levinson et al. [1983] and Poskitt & Chung [1994]). Hence, there exists a separate field of literature dealing with this model, starting with blackwell & Koopmans [1975] and Heller [1965]. More recently, estimation methods have been discussed by Voina [1988], Leroux [1992], and Qian & Titterington [1992].
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© 1997 Springer-Verlag Berlin Heidelberg
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Krolzig, HM. (1997). VARMA-Representation of MSI-VAR and MSM-VAR Processes. In: Markov-Switching Vector Autoregressions. Lecture Notes in Economics and Mathematical Systems, vol 454. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51684-9_4
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DOI: https://doi.org/10.1007/978-3-642-51684-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63073-9
Online ISBN: 978-3-642-51684-9
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