Estimating Variance of Parameter Estimators by Supplemented Expectation Maximization and Gibbs Sampling Algorithm in Regime-Switching Jump Model

• Main Authors: Sheng-jie Wu, 吳聲杰
• Other Authors: Shih-kuei Lin
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/99s839

碩士 === 國立高雄大學 === 統計學研究所 === 97 === Fuh and Lin (2004) proposed a Markov-switching jump model in which economic states are assumed to describe the possibly different arrival rates of the information. In this research, we investigate the model in two states setting, the so called regime-switching jump model. Estimation of the model parameters by maximum likelihood estimation is often difficult, however, since the jump sizes, the jump frequencies and the states are hidden variables. In such an incomplete data problem, we estimate the parameters by using expectation maximization (EM) algorithm and Gibbs sampling algorithm, and the variance of parameter estimators by using supplemented EM (SEM) algorithm and Gibbs sampling algorithm. In the empirical analysis, we investigate all thirty Dow Jones Industrial stocks to find more suitable model for a jump diffusion model, a regime-switching jump model with independent jump sizes and a regime-switching jump model with dependent jump sizes by asymptotic normality of the maximum likelihood estimator, and likelihood ratio test.