Theory And Analysis Of Returns Of IBM Asset Based On Hidden Markov Model

Some kinds of underlying financial data are usually difficult to observed, which probably has an effect on the development of observed process. The hidden states that always vary from time to time are not assumed to be independent. Hidden Markov Model (HMM) can be used to deal with the relationship between an observed process and an underlying process.Taking the theory of HMM and its relative information as the theory basis, this paper explores a hidden markov model with a normal distribution assumption, and discusses the algorithm of a category of problems on the basis of traditional discrete HMM. In the paper, we introduce MLE and EM algorithm to maximize HMM likelihood, use the penalized distance function to estimate the number of states of a HMM, and apply our procedure to the data of the daily log returns of IBM, collected by Ruey S. Tsay from the Center for Research in Security Prices (CRSP) of the University of Chicago.