# 14. Markov Chain Monte Carlo Methods

Published Online: 28 JAN 2011

DOI: 10.1002/9781118032466.ch14

Copyright © 2010 John Wiley & Sons, Inc. All rights reserved

Book Title

## Time Series: Applications to Finance with R and S-Plus, Second Edition

Additional Information

#### How to Cite

Chan, N. H. (2010) Markov Chain Monte Carlo Methods, in Time Series: Applications to Finance with R and S-Plus, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032466.ch14

#### Publication History

- Published Online: 28 JAN 2011
- Published Print: 13 SEP 2010

#### Book Series:

#### ISBN Information

Print ISBN: 9780470583623

Online ISBN: 9781118032466

- Summary
- Chapter

### Keywords:

- Bayesian statistics;
- Gibbs sampling;
- jump-diffusion model;
- likelihood function;
- Markov Chain Monte Carlo (MCMC) method;
- Metropolis-Hastings Algorithm;
- time series

### Summary

Bayesian inference is an important area in statistics. This chapter briefly introduces the essence of Bayesian statistics with reference to time series. In particular, it discusses the celebrated Markov Chain Monte Carlo (MCMC) method in detail and illustrates its uses via an example. There are many ways to specify a prior distribution in the Bayesian setting. Some prefer non-informative priors and others prefer priors that are analytically tractable. Given a likelihood function, the conjugate prior distribution is a prior distribution such that the posterior distribution belongs to the same class of distribution as the prior. The chapter summarizes some of the commonly used conjugate priors. It talks about the Metropolis-Hastings Algorithm and explains Gibbs sampling. Gibbs sampling is used to estimate parameters of a jump-diffusion model and examine the impact of jumps in major financial indices. The chapter presents a case study on ‘The impact of jumps on Dow Jones’.

#### Controlled Vocabulary Terms

Bayesian inference; Gibbs sampler; jump-diffusion model; likelihood principle; Metropolis-Hastings algorithm; statistics