Abstract
This first chapter is devoted to a general introduction into the Markov-switching vector autoregressive (MS-VAR) time series model. In Section 1.2 we present the fundamental assumptions constituting this class of models. The discussion of the two components of MS-VAR processes will clarify their on time invariant vector auto-regressive and Markov-chain models. Some basic stochastic properties of MS-VAR processes are presented in Section 1.3. Finally, MS-VAR models are compared to alternative non-normal and non-linear time series models proposed in the literature. As most non-linear models have been developed for univariate time series, this discussion is restricted to this case. However, generalizations to the vector case are also considered.
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In the case of two regimes, Potter [1990], [1993] proposed to call this class of non-linear, non-normal models the single index generalized multivariate autoregressive (SIGMA) model.
In threshold autoregressive (TAR) processes, the indicator function is defined in a switching variable z t-d , d ≥ 0. In addition, indicator variables can be introduced and treated with error-in-variables techniques. Refer for example to Cosslett & Lee [1985] and Kaminsky [1993].
If F(·) is even, e.g. F(y t-d – r) = 1 – exp {-(y t-d – r)2}, a generalized exponential autoregressive model as proposed by Ozaki [1980] and Haggan & Ozaki [1981] ensues.
The reader is referred to Hamilton [1994a] for an excellent introduction into the major concepts of Markov chains and to Titterington, Smith & Makov [1985] for the statistical properties of mixtures of normals.
Models where the regime is switching between deterministic and stochastic trends are considered by McCulloch & Tsay [1994a].
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© 1997 Springer-Verlag Berlin Heidelberg
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Krolzig, HM. (1997). The Markov-Switching Vector Autoregressive Model. 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_2
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DOI: https://doi.org/10.1007/978-3-642-51684-9_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63073-9
Online ISBN: 978-3-642-51684-9
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