On White Noises Driven by Hidden Markov Chains

Hidden Markov models form an extension of mixture models which provides a¯exible class of models exhibiting dependence and a possibly large degree of variability. We show how reversible jump Markov chain Monte Carlo techniques can be used to estimate the parameters as well as the number of components of a hidden Markov model in a Bayesian framework. We employ a mixture of zero-mean normal distributions as our main example and apply this model to three sets of data from ®nance, meteorology and geomagnetism.

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“…Francq and Roussignol (1997) proposed k 2 with their MLE yielding a log-likelihood of about À6101. In Fig.…”

Section: Some Resultsmentioning

confidence: 99%

Bayesian Inference in Hidden Markov Models Through the Reversible Jump Markov Chain Monte Carlo Method

Robert

Rydén

Titterington

2000

Journal of the Royal Statistical Society Series B: Statistical Methodology

190

145

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“…That algorithm may be more suitable for models with many free parameters, e.g., when many variables are considered and the number of states is larger than 2 or 3. The properties of Gaussian ML estimation in a univariate model of type (2.4) (that is, the process is white noise conditional on a given state of the Markov chain) were discussed by Francq and Roussignol (1997). Very general asymptotic estimation results for stationary processes are available in Douc et al (2004).…”

Section: Estimationmentioning

confidence: 99%

Structural vector autoregressions with Markov switching

Lanne

Lütkepohl

Maciejowska

2010

Journal of Economic Dynamics and Control

182

158

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a b s t r a c tIt is argued that in structural vector autoregressive (SVAR) analysis a Markov regime switching (MS) property can be exploited to identify shocks if the reduced form error covariance matrix varies across states. The model setup is formulated and discussed and it is shown how it can be used to test restrictions which are just-identifying in a standard structural vector autoregressive analysis. The approach is illustrated by two SVAR examples which have been reported in the literature and which have features that can be accommodated by the MS structure.

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“…The mathematical properties of a process generated by a finite Markov mixture distribution have been studied for specific processes obeying conditions Y4 and S4 such as hidden Markov chain models (Blackwell and Koopmans, 1957;Heller, 1965), white noise driven by a hidden Markov chain (Francq and Roussignol, 1997), discrete-valued time series generated by a hidden Markov chain (MacDonald and Zucchini, 1997), Markov mixtures of normal distributions (Krolzig, 1997), and Markov mixtures of more general location-scale families, where Y t = µ St + σ St ε t , with ε t being an i.i.d. process (Timmermann, 2000).…”

Section: Basic Definitionsmentioning

confidence: 99%