This article details a Bayesian analysis of the Nile river flow data, using a simple state space model. This allows the article to concentrate on implementation issues surrounding this model. For this data set, Metropolis-Hastings and Gibbs sampling algorithms are implemented in the programming language Ox. The Markov chain Monte Carlo methods only provide output conditioned upon the full data set. For filtered output, conditioning only on past observations, the particle filter is introduced. The sampling methods are flexible, and this advantage is used to extend the model to incorporate a stochastic volatility process. The volatility changes both in the Nile data, and for comparison 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 identifiable, and which elements are estimated with less precision.
Bos, C. S. (2011). A Bayesian Analysis of Unobserved Component Models Using Ox. SSRN. https://doi.org/10.2139/ssrn.1776046