Date of Graduation


Document Type


Degree Name

Master of Science in Statistics and Analytics (MS)

Degree Level



Statistics and Analytics


Giovanni Petris

Committee Member

John Tipton

Second Committee Member

Jyotishka Datta


Hidden Makrov Models, Sequential Monte Carlo Methods, State Space Models, Time Series Analysis


In many applications data are collected sequentially in time with very short time intervals between observations. If one is interested in using new observations as they arrive in time then non-sequential Bayesian inference methods, such as Markov Chain Monte Carlo (MCMC) sampling, can be too slow. Increasingly, state space models are being used to model nonlinear and non-Gaussian systems. The structure of state space models allows for sequential Bayesian inference so that an approximation to the posterior distribution of interest can be updated as new observations arrive. In special cases, the exact posterior distribution can be updated through conjugate Bayesian inference. However, for the general state space model this is not possible. In quantitative finance hidden Markov models have been used to analyze and forecast percent log returns of an asset or a group of assets. In this thesis the Liu and West [2001] auxiliary particle filter is applied to sequentially update the posterior distribution of a hidden Markov model with unknown state and observation distribution parameters.