The marginal likelihood of Structural Time Series Models, with application to the euroareaa nd US NAIRU
AbstractWe propose a simple procedure for evaluating the marginal likelihood in univariate Structural Time Series (STS) models. For this we exploit the statistical properties of STS models and the results in Dickey (1968) to obtain the likelihood function marginally to the variance parameters. This strategy applies under normal-inverted gamma-2 prior distributions for the structural shocks and associated variances. For trend plus noise models such as the local level and the local linear trend, it yields the marginal likelihood by simple or double integration over the (0,1)-support. For trend plus cycle models, we show that marginalizing out the variance parameters greatly improves the accuracy of the Laplace method. We apply this ethodology to the analysis of US and euro area NAIRU.
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Bibliographic InfoPaper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 21-08.
Date of creation: Jan 2008
Date of revision: Jan 2008
Marginal likelihood; Markov Chain Monte Carlo; unobserved components; bridge sampling; Laplace method; NAIRU;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-09-13 (All new papers)
- NEP-ECM-2008-09-13 (Econometrics)
- NEP-ETS-2008-09-13 (Econometric Time Series)
- NEP-ORE-2008-09-13 (Operations Research)
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