本文考慮門檻隨機波動模型與門檻隨機波動跳躍模型之貝氏分析。在給定主觀先驗分佈下，以馬可夫鏈蒙地卡羅方法估計模型中之未知參數，進而討論未來觀測值與風險值之預測。關於隨機跳躍部份，本文亦分別考慮跳躍幅度與跳躍機率可能會隨門檻值改變的情形。實務分析中，可以 DIC 準則做為模型選擇的依據。 This thesis presents a threshold stochastic volatility model and a threshold stochastic volatility jump model with unknown threshold from a Bayesian viewpoint. Bayesian inferences of the unknown parameters are obtained with respect to a subjective prior distribution via Markov chain Monte Carlo (MCMC) method. In addition, the value at risk (VaR) of the distribution of the next future observation is also developed based on predictive distribution. For jump component in the threshold stochastic volatility model, we consider the situations where the jump size and jump probability might be changed by the threshold value. In practice, the deviance information criterion (DIC) is suggested for model selection.
