Journal of Statistical Software

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Sample volume 1
Title A Bayesian Analysis of Unobserved Component Models Using Ox
Author Bos Charles S.
This article details a Bayesian analysis of the Nile river ow data, using a similar
state space model as other articles in this volume. For this data set, Metropolis-Hastings and Gibbs sampling algorithms are implemented in the programming language Ox. These Markov chain Monte Carlo methods only provide output conditioned upon the full data set. For ltered output, conditioning only on past observations, the particle lter is
introduced. The sampling methods are exible, and this advantage is used to extend the
model to incorporate a stochastic volatility process. The volatility changes both in the
Nile data and also in daily S&P 500 return data are investigated. The posterior density
of parameters and states is found to provide information on which elements of the model
are easily identi able, and which elements are estimated with less precision.
Keywords state space methods, unobserved components, Bayes, stochastic volatility.
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