| We here introduce an architecture named Hidden Markov Models to establish a pre-dictive model to analyze USD/CNY exchange rate time series. HMM has been extensively used in speech recognition research area in the1980s and now is gradually gaining its pop-ularity in econometrics and financial engineering area.In my dissertation, Hidden Markov Models model time dependency of exchange rate return series as a first-order Markov model, however, the states of the Markov Chain is hidden, i.e. unobservable.Firstly, in Chapter1, this dissertation discusses the background of HMM and its previous applications to Finance area, as well as some preliminaries for establishing the HMM. Then, in Chapter2, the probability theoretical framework of HMM is established and the three fundamental problems,i.e. evaluation, decoding and parameter estimation are investigated. Meanwhile, this chapter also gives the corresponding algorithm of the three problems. Further more,in chapter3, we assign prior distributions to the parameters of the Hidden Markov Model and use a framework of Bayesian Inference to estimate the posterior mean of the parameters. Here, we mainly discussed Bayesian Inference for the Hidden Markov Model with the observations'state-dependent distribution following Nor-mal distribution. Further more, the conjugate Dirichlet prior of the transiton probability matrix is used, so are the conjugate priors of the mean and variance parameters of Normal distribution. After establishing a Bayesian framework, we apply the MCMC algorithm to estimate the posteriors of the model parameters. In Chapter4, the Hidden Markov Model is applied to model the the log return time series of USD/CNY exchange rate. The resulting parameters estimated by Baum-Welch and MCMC algorithm are compared and some meaningfull findings are discovered. Finally, in the last chapter, we conclude the performance of the HMM used to model the exchange rate data and point out some related topics for further research. |
PDF Full Text Request