This article considers Markov chain simulation and statistical analysis of high-dimensional financial time series. In particular, we discuss Markov chain Monte Carlo methods, for example, Gibbs sampling and Metropolis-Hasting algorithm, and multivariate volatility models with applications in finance. Real examples are used to demonstrate statistical applications of the methods discussed in risk management and volatility estimation. WIREs Comp Stat 2011 3 289–315 DOI: 10.1002/wics.168
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