Hidden Markov Model Can Be Used To Update The Promotion And Application Of Em Algorithm

EM algorithm is the main algorithm when estimating parameters in a Hidden Markov Model(HMM). This paper discuss about the online parameter estimation of discrete time HMM and give an online version of EM algorithm for HMM under the assumption that state conditional probability density function is a mixture of distribu-tions beglong to exponential families. This is a generalization of the results obtained for HMM with state transition probability function and state conditional probability density function both belong to exponential families. The complete estimation proce-dure is given when the state conditional pdf is mixture of normal distributions. Then the online EM algorithm is also given when the assumption of hidden states changes into second-order homogeneous Markov chain. Empirical study about the volatility of stock index’s return is done in the last chapter.