Gong, Chen
(2019)
Particle Gibbs Methods in Stochastic Volatility Models.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
The Stochastic Volatility (SV) model and the Multivariate Stochastic Volatility (MSV) model are powerful tools for modeling the volatility of stock price data. A lot of research has been done in the past 40 years. One popular method is to represent the SV as a hidden Markov model and employ the Bayesian inference through the Markov Chain Monte Carlo (MCMC) method. Sampling the hidden states in the SV model from the full conditional distribution is the key part in MCMC. Several particle methods had been developed to approximate the hidden states, such as the Sequential Monte Carlo (SMC) and Particle MCMC. However, these methods suffer from the path degeneracy problem. The Particle Gibbs with Ancestor Sampling (PGAS) was introduced to deal with the path degeneracy in 2014 and it made the MCMC algorithm efficient. However, we believe that the efficiency of MCMC still can be improved by choosing a suitable prior distribution for the parameters in the SV model. In this thesis, we explore the potential reason, which leads to the low efficiency problem, and propose a new method to deal with the SV model through the PGAS algorithm. In our proposed method, we employ the bivariate normal distribution as prior distribution for the parameters in the state equation. The negative correlation between the two parameters can be explained by setting a negative correlation coefficient in the prior distribution. Consequently, the efficiency of the algorithm is improved significantly after sampling parameters out jointly through the Random Walk Metropolis Hastings (RWMH). However, sometimes it is difficult to find a good proposal distribution for RWMH in practice. Thus, we apply the adaptive MCMC to our proposed method to further improve the algorithm. Moreover, we extend our proposed method to the MSV model and get a high efficiency algorithm. We provide theoretical details of particle method to justify the validity of the proposed methods. Numerical experiments, including simulation studies and applications to the S&P 500 index data and some banks' stock data, are presented to demonstrate the good performances of the proposed methods.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
26 September 2019 |
| Date Type: |
Publication |
| Defense Date: |
2 August 2019 |
| Approval Date: |
26 September 2019 |
| Submission Date: |
16 September 2019 |
| Access Restriction: |
1 year -- Restrict access to University of Pittsburgh for a period of 1 year. |
| Number of Pages: |
145 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Statistics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Stochastic Volatility, Hidden Markov model, Particle Gibbs with Ancestor Sampling, Efficient Markov Chain Monte Carlo, Multivariate Stochastic Volatility model |
| Date Deposited: |
26 Sep 2019 12:59 |
| Last Modified: |
26 Sep 2020 05:15 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/37650 |
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