Adaptive particle filter in hidden Markov models : a new approach and its applications
- Hidden Markov models have been widely used in many fields, such as bioinformatics, econometrics, targets tracking and population genetics. The particle filter, also known as sequential Monte Carlo method, is a powerful tool for latent state filtering of the hidden Markov models. In this thesis, we propose a new methodological advancement, the adaptive particle filter, for the problem of joint parameter estimation and latent state filtering of hidden Markov models. The adaptive particle filter is a hybrid algorithm that combines particle filter and a new MCMC scheme, called sequential substitution, to provide an efficient estimate for function of the parameter and latent state, and further give a consistent estimator of Monte Carlo standard error. Specifically we approximate the posterior distribution of the parameters and latent states by a representative population of N parameter atoms, in which each parameter atom contains P weighted 'particles' where each particle consists of a latent state generated by particle filter. Sequentially updated by the sequential substitution MCMC scheme, the representative population converges weakly to i.i.d samples from the target posterior distribution in the limit of infinite many iterations. By representing the adaptive particle filter as a standard sequential substitution on the extended space of joint parameter atoms and latent state particles, we establish the asymptotic normality of the estimate for the functional posterior mean and the consistency of the Monte Carlo standard error estimator based on the theoretical result of sequential substitution. In addition, we propose the Markov chain restart to deal with the case of long observed time series. Markov chain restart suggests using the representative population of parameter and latent state generated by adaptive particle filters up to time t as approximation of posterior distribution; then particle filters performed for newly proposed parameter atoms at time t + △t can start from the middle of time t. Markov chain restart greatly reduces the computation cost of adaptive particle filters and enables performing more sequential substitution iterations. It also increases the acceptance rate of the MCMC update in adaptive particle filters. Furthermore we demonstrate the effectiveness of adaptive particle filter and Markov chain restart algorithm with simulation results on an example of a highly nonlinear hidden Markov model. Finally as an application in econometrics, we apply our approach on parameter estimation and latent volatility filtering for the jump-diffusion models using both asset returns and option prices.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Statistics.
|Lai, T. L
|Lai, T. L
|Wong, Wing Hung
|Wong, Wing Hung
|Statement of responsibility
|Submitted to the Department of Statistics.
|Thesis (Ph.D.)--Stanford University, 2016.
- © 2016 by Yuming Kuang
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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