A Study And Application On Doubly Stochastic Series Models AR(1)-ARMA(p,q)

Time series as a common data analysis and prediction of the method,have a widelyrange of applications.In order to better estimate and describe the diferent areas of sta-tistical phenomenon, the research and application of nonlinear time series had arousedpeople’s great attention.In such condition,a special kind of nonlinear time series-a doublystochastic time series was put forward by Swedish scholars D.T j sheim in1986.Becausethe model is more complex,people just studied a few of the basic problem about some of thesimple model.The model of parameter estimation,the prediction problem and determiningorder have been researched less,so this paper quotes from a new analysis method-bayesiananalysis to study the parameter estimation of model.First of all,this paper studied the parameter estimation of the doubly stochastic timeseries of AR(1)-ARMA(1,1)and AR(1)-ARMA(p,q).Assuming the existence of second or-der stationary solution,we can estimate the parameters of the model by the bayesian the-ory and MCMC method,In theory,we get the posterior distribution of the parameters andunobserved data ytand bayesian estimation in the second loss function.Meanwhile,usingWinbugs software to simulate and analyze,we got the mean of posterior distribution pa-rameters of the model,standard deviation,median,95%confdence interval and other sta-tistical information,where the mean of posterior distribution is the bayesian estimation ofparameters,this is also testifed that using this method to estimate the parameters is thefeasible.Finally,this paper studied forecasting for the model.The coefcient of model of thefrst time series is a stationary stochastic series of ARMA and this stochastic series isinvisible,so the forecast analysis is more difcult for this model.But the earlier in the pa-per, parameters estimation had come out,so that we can assume that the parameters ofthe model and other information were known,to study the model of forecast analysis.Thispaper combined the traditional least mean square error prediction with parameter esti-mation,which got the results of the analysis on the step forecast. Bayesian method combining with the prior distribution,so we research problems morein line with the reality.After our study about AR(1)-ARMA(p,q),we obtained the bayesianestimation of model parameters and step forecast value,this result proved bayesian andMCMC method to estimate parameters is a kind of efective and feasible method,alsoprovides a new choice for the parameter estimation.