Bayesian Inference and Model Selection for Double Hysteretic Heteroskedastic Models

• Main Authors: Truong Buu Chau, 張寶珠
• Other Authors: Cathy W. S. Chen
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/65727933638108860072

博士 === 逢甲大學 === 統計學系統計與精算碩士班 === 104 === Nonlinear time series models play an important role in describing and forecasting time series data. A natural approach to modeling time series data with nonlinear models is the threshold model, which is defined by different regimes for different dynamic behaviors. However, any disturbance in a time series may lead to a trickle-down effect, and the problem could persevere for a long time, because as the structure of regimes appears not to switch immediately, a hysteretic region may exist. Therefore, this thesis proposes two kinds of nonlinear hysteretic autoregressive heteroskedastic models for two different types of time series: financial time series and integer-valued time series. This study develops Bayesian methods for these two families of models, which include parameter estimation, forecasting, diagnosis, and model selection. We describe the development of time series models and methods in the following three topics. The first part of this thesis introduces a hysteretic autoregressive model with a GARCH specification (HAR-GARCH) model under a skew Student’s t-error distribution to describe nonlinear and asymmetric models for financial time series. With an integrated hysteresis zone, this model allows for the delay of both conditional mean and conditional volatility switching in a regime where the hysteresis variable lies in a hysteresis zone. We propose Bayesian inference and forecasting via an adaptive Markov Chain Monte Carlo (MCMC) sampling scheme, which allows simultaneous inferences for all unknown parameters, including threshold values and a delay parameter. Employing simulation studies and four major stock basis series helps illustrate this methodology. To implement model selection, we conduct a numerical approximation of the marginal likelihoods to posterior odds and find strong evidence of the hysteretic effect and some asymmetric heavy-tailness. Moreover, we utilize Value-at-risk forecasting via the computational Bayesian framework for two historical simulation methods and six models for comparison. The second part of this thesis provides model selection via three criteria among competing nonlinear GARCH models, because the odds ratios method is time consuming. The purpose of this study is to select a nonlinear heteroskedastic model with an appropriate switching mechanism for financial time series. While the threshold autoregressive (TAR-GARCH) models are popular nonlinear models for capturing the well-known asymmetric phenomenon in financial market data, their switching mechanisms are different from those of HAR-GARCH, in which the regime switching may remain unchanged when the hysteresis variable lies in a hysteresis zone. The three criteria used for comparing models with fat-tailed and/or skewed errors are Deviance Information Criteria (DIC), Bayesian predictive information criteria, and the asymptotic version of Bayesian predictive information. This study designs the Bayesian model comparison among competing models through an adaptive MCMC sampling scheme, with a simulation experiment that illustrates good performance in estimation and model selection. Additionally, we demonstrate the proposed method in an empirical study of 12 international stock markets, providing strong support for both models with skew fat-tailed innovations. In the third part we propose a new model for time series of counts, the hysteretic Poisson integer-valued generalized autoregressive conditionally heteroskedastic (INGARCH) model, which has an integrated hysteresis zone in the switching mechanism of the conditional expectation. Our modeling framework provides a parsimonious representation of the salient features of time series of counts, such as discreteness, over-dispersion, asymmetry, and structural change. We adopt Bayesian methods with a MCMC sampling scheme to estimate model parameters and utilize the Bayesian information criteria for model comparison. We then apply the proposed model to five real time series of criminal incidents recorded by the New South Wales Police Force in Australia. Simulation results and empirical analysis highlight the performance of hysteresis in modeling the time series count data.