A Markov Chain Model With High-order Hidden Process And Mixture Transition Distribution

Markov model was put forward since twentieth Century, which was almost could be applied to all field of the predictive analysis. However, the traditional first-order Markov chain limited its predictive ability. In practical applications, the higher-order Markov chain was not to be optimistic about people, because of its parameter set is too large, or the number of parameters increases with the order number increase exponentially. This situation was often regarded as the big bang of parameters. This not only increased the complexity of the state space, while also reducing the prediction accuracy of the parameters. Aiming at the defects of the higher-order Markov model, Raftery proposed a new model in 1985, namely mixture transition distribution model or MTD model for short. In the MTD model, the effect of each lag on the prediction of the current observation was considered separately, and it was used to approximate high-order Markov model with far lower dimension of parameter space. On the basis of MTD model, the first-order Markov chain was introduced to the hidden process, which is a first-order Markov chain.This thesis is mainly focus on higher-order Markov model which is contents latent variable and its parameter estimation problems. On the basis of previous analysis, we further study a Markov model with high-order hidden process and MTD model. The main contents include:1. Based on previous research, we continue to improve the model so that it can adapt to more actual situations. We suppose that the latten variables submit to higher-order Markov chains, and then, construct an double-chain higher-order Markov model.2. For the MTD model with high-order hidden process, we use the table to illustrate that our model is not only expand on the order and the relationship between each of the nested models. Under certain conditions, this simple model can be evolved into other Markov models.3. This thesis use the expectation maximization(EM) algorithm to calculate the estimation of every parameter, and introduce the idea of scaling method in the process of parameter estimation, so that it can amplify coefficient of every step and not be regarded as zero lead to cross-border appears distortion of the outcomes through computer programming.4. The measured data of impulse noise in the power line communication channel are used to experiment. And comparing the prediction effects of these models, and giving the results.