Abstract
This article details a Bayesian analysis of the Nile river flow 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 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 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.
Highlights
In this article we analyze the Nile data from a Bayesian perspective using Ox (Doornik, 2009)
The added value of a Bayesian analysis, is that full information on the uncertainty of the parameters is obtained from the posterior density, and that problems with multimodality of the density surface are tackled more
In order to analyse the local level model for the Nile data using a Markov chain Monte Carlo (MCMC) setup, first an analysis of the parameters occuring in the model and their possible sampling schemes is needed
Summary
Of Econometrics and Operations Research, VU University Amsterdam, and Tinbergen Institute. Tinbergen Institute is the graduate school and research institute in economics of Erasmus University Rotterdam, the University of Amsterdam and VU University Amsterdam. Duisenberg school of finance is a collaboration of the Dutch financial sector and universities, with the ambition to support innovative research and offer top quality academic education in core areas of finance
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