The Bayesian Analysis Of MA(q) Model

The establishment of the order,the estimation of parameters for the model and the ability for forecasting seem very important for setting up a model in time series. The first one provides a model to simulate the numerical information and the latter one estimate the future numerical information using the model which is the main purpose in analysising the time series.At present, the theory for analsising time series model is complex because of classical statistics method which concerns plenty of principles of sampling. The Bayes can solve it easily but complex integral operation restrict its development. However, difficulities can be solved with the development of computing and the amelioration of Bayes technique, which facility posterior inference and advance Bayesian time series,. An approximate model recomposed by moving average model and an approximate likelihood of model are introduced successfully in this thesis to figure out the integral problem. Consequently,we can establish the order of the model, estimate the parameters and forecast using Bayes methods.Concretely,this thesis discuss the order of the model by introducing an approximate model recomposed by moving average model.We draw the result from mixmum Bayes expected loss in the level of general priors distribution and quadratic loss function.In succession, the Bayes estimation for parameters of the modle whose order has been established already are worked out under the minmum posterior risk,which give birth to the Baysesian analysis based on Normal-Gamma conjugate prior distribution and Jeffrey' nonimformative priors distribution.At last, according to the definition of Bayes predictive distribution , the exact distribution for one step are educed.