August 2010
Intermediate to advanced
701 pages
18h 7m
English
Chapter 12
Markov Chain Monte Carlo Methods with Applications
Advances in computing facilities and computational methods have dramatically increased our ability to solve complicated problems. The advances also extend the applicability of many existing econometric and statistical methods. Examples of such achievements in statistics include the Markov chain Monte Carlo (MCMC) method and data augmentation. These techniques enable us to make some statistical inference that was not feasible just a few years ago. In this chapter, we introduce the ideas of MCMC methods and data augmentation that are widely applicable in finance. In particular, we discuss Bayesian inference via Gibbs sampling and demonstrate various applications of MCMC methods. Rapid developments in the MCMC methodology make it impossible to cover all the new methods available in the literature. Interested readers are referred to some recent books on Bayesian and empirical Bayesian statistics (e.g., Carlin and Louis, 2000; Gelman, Carlin, Stern, and Rubin, 2003).
For applications, we focus on issues related to financial econometrics. The demonstrations shown in this chapter represent only a small fraction of all possible applications of the techniques in finance. As a matter of fact, it is fair to say that Bayesian inference and the MCMC methods discussed here are applicable to most, if not all, of the studies in financial econometrics.
We begin the chapter by reviewing the concept of a Markov process. Consider a stochastic ...
