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Modeling Non-Gaussian Time-correlated Data Using Nonparametric Bayesian Method

Xu, Zhiguang
http://rave.ohiolink.edu/etdc/view?acc_num=osu1406068732

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Statistics.
This dissertation proposes nonparametric Bayesian methods to study a large class of non-Gaussian time-correlated data, including non-Gaussian time series and non-Gaussian longitudinal datasets. When a time series is noticeably non-Gaussian, classical methods with Gaussian innovations will yield poor fits and forecasts, but the joint distribution of a non-Gaussian time series is often difficult to specify. To overcome this difficulty, we propose the copula-transformed AR (CTAR) model. This model utilizes the copula method to determine the joint distribution of the observed series by separating the marginal distribution from the serial dependence. In implementation, we model the observed series as a nonlinear, nonparametric transformation from a latent Gaussian series. The marginal distribution of the observed series follows a nonparametric Bayesian prior distribution having large support, and therefore any non-Gaussian distribution can be well approximated. The dependence structure of the observed series is characterized indirectly through the latent Gaussian time series, so that we can borrow some classic Gaussian time series modeling methods to model the serial dependence. We also extend the proposed nonparametric Bayesian copula methods to model stationary time series with changing conditional volatility by developing copula-transformed AR-GARCH (CTAR-GARCH) model, which describes the observed series as a nonlinear, nonparametric transformation from an AR-GARCH latent series. We conduct simulations and show the CTAR and CTAR-GARCH models' advantages in capturing non-Gaussian marginal and predictive distributions. We also fit the CTAR-GARCH models to stock index return series and conclude that they yield better predictions than the classical AR-GARCH models with Gaussian innovation. We further extend our models to the non-Gaussian longitudinal analysis setting. We model an observed within-subject response series as a transformation from a latent Gaussian series. The latent series specifies the within-subject dependence structure and the transformation function specifies marginal distribution of response variable. Similar to CTAR models, a marginal distribution of the response variable has a nonparametric Bayesian prior distribution and is therefore flexible in shape. We conduct simulations and study a 100km-race real dataset where the response variable is noticeably non-Gaussian. The data analysis demonstrates the advantage of copula-transformed models' performance in model fitting and prediction compared with the Gaussian-based models when the data is truly non-Gaussian and when the mean function is correctly specified. We also study the situations where the mean function shifts in the out-of-sample data. We find that the model's predictive performance for individuals is impacted by the shifts. The copula-transformed models are more sensitive to the shift than the Gaussian-based models. We also study the predictive performance of the contrasts. The models' predictive performance remains fairly robust to the shifts, and the copula-transformed models outperform the Gaussian-based models in contrast predictions. The proposed method can be extended in many directions, including using other transformation functions (e.g., a transformation using Polya tree prior).
Steven MacEachern (Advisor)
Xinyi Xu (Advisor)
Mario Peruggia (Committee Member)
Statistics
time series, longitudinal data, copula, nonparametric Bayesian method

Recommended Citations

Citations

  • Xu, Z. (2014). Modeling Non-Gaussian Time-correlated Data Using Nonparametric Bayesian Method [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406068732

    APA Style (7th edition)

  • Xu, Zhiguang. Modeling Non-Gaussian Time-correlated Data Using Nonparametric Bayesian Method. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1406068732.

    MLA Style (8th edition)

  • Xu, Zhiguang. "Modeling Non-Gaussian Time-correlated Data Using Nonparametric Bayesian Method." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406068732

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.