Bayesian Analysis of Non-Gaussian Stochastic Processes for Temporal and Spatial Data
Jiangyong Yin · OhioLink ETD Center (Ohio Library and Information Network) · 2014
The Gaussian stochastic process is the most commonly used approach for modeling time series and geo-statistical data.The Gaussianity assumption, however, is known to be insufficient or inappropriate in many problems.In this dissertation, I develop specific non-Gaussian models to capture the asymmetry and heavy tails of many real-world data indexed in the time, space or space-time domain.Chapter 2 of this dissertation deals with a particular non-Gaussian time series model -the stochastic volatility model.The parametric stochastic volatility model is a nonlinear state space model whose state equation is traditionally assumed to be linear.Nonparametric stochastic volatility models provide great flexibility for modeling financial volatilities, but they often fail to account for useful shape information.For example, a model may not use the knowledge that the autoregressive component of the volatility equation is monotonically increasing as the lagged volatility increases.I propose a class of additive stochastic volatility models that allow for different shape constraints and can incorporate leverage effect, the asymmetric impacts of positive and negative return shocks on volatilities.I develop a Bayesian model fitting algorithm and demonstrate model performances on simulated and empirical datasets.Unlike general nonparametric models, the proposed model sacrifices little when the true volatility equation is linear.In nonlinear situations, the proposed method improves the model fit and the ability to estimate volatilities over general, First and foremost, I owe my deepest gratitude to my advisors, Peter Craigmile and Xinyi Xu, for taking me in as their student since my very first year at Ohio State and devote so much of their time to the individual studies that we did together, for their continued guidance and coaching throughout the past five years even when we were oceans or cities apart, for their amazing patience and tolerance for my often wrong opinions and sometimes unreasonable requests, for imparting their knowledge and wisdom to me without any reservations, and for their financial support for my academic growth.I would like to thank my committee member, Professor Steven MacEachern, for his guidance and his invaluable suggestions during my candidacy exam which has contributed to the development of part of this dissertation.I would also like to thank Dr. Yoonkyung Lee, who was on my candidacy exam committee, for her time and for allowing me to sit in her classes asking numerous questions.I specially want to