Censored Time Series Model And Variable Selection Based On EM Algorithm

Model selection has always been an important and hot topic in statistical research,among which Bayes-based variable selection is unique.This type of method introduces different prior information,and then combines the likelihood to obtain efficient statistical inference.For many important parametric models and non-parametric models,a large number of literatures have used Bayesian variable selection methods.Time series analysis is an important branch of statistical research.It takes the data formed by the state of things at different times as the research object,and conducts research and analysis through its characteristics to discover the changing laws of things.Censored time series data often appear in our daily lives,and the modeling and analysis of this type of data is of great significance.This paper combines Bayesian variable selection and censored time series quasi-likelihood,constructs Bayesian variable selection of time series models under censored data,and uses EM algorithm to solve calculation problems,which can quickly obtain efficient estimates of model parameters.For the following two parts.The first part introduces the censored autoregressive model and its conditional logarithmic quasi-likelihood,and then introduces the Bayesian method to obtain the posterior distribution of the quasi-likelihood through continuous spike and slab priors.The parameter estimation and variable selection of the autoregressive model are obtained by using the EM algorithm,which reduces the calculation amount of the MCMC method.In the model research,a higher rate of correct model selection is obtained,which verifies the effectiveness of this method.Finally,the proposed method is applied to Cloud Ceiling data for analysis.The second part studies the variable selection of the censored time series model with exogenous variables and autoregressive structure.Given a suitable prior distribution,the posterior distribution of variable selection is obtained through posterior inference,and the EM algorithm is used to maximize the posterior.Distribution and obtain the estimation of covariate parameters and autoregressive parameters and variable selection.The effectiveness of this method was verified in the simulation,and the simulation results performed well.With the increase of the sample size,the correct selection rate of the model gradually increased and the mean square error of the model fitting became increasingly small.Finally,the proposed method is applied to the phosphorus concentration data in river water for analysis.