Bayesian Forecasting Model For Economic Time Series And Its Application

In economic field, the time series models are important methods in describing and forecasting the objective economic process. However, when put them into application, because of the particularity of economic field, we often encounter many difficulties in the time series models analysis by using the traditional frequency statistical method. Therefore, this paper describes a technique, economic forecasting with Bayesian time series models, which has proved over the past several years to be an attractive alternative in many situations to the use of traditional economtric models or other time series techniques.This paper mainly deals with the estimated procedure for classical time series models under Bayesian inference framework, and their application with posterior computations is performed by Markov chain Monte Carlo (MCMC) Method. This includes the Bayesian inference theory about the Autoregressive model (AR), the moving average model (MA), the Autoregressive moving average model (ARMA) and the Vector Autoregressive model (VAR).Firstly, we begined with the simplest AR model, and analyzed its mathematical model and condition likelihood function. According to its statistical structure of likelihood function, constructed their Bayesian estimation under the normal-Gamma conjugate prior distribution. Derived the forecasting distribution of AR(p) models with one future observation. Last, implemented simulation analysis of the AR(2) model using WinBUGS.Secondly, we analyzed MA model with Bayesian method. Begining with the first order MA model, analyzed it's mathematical model and condition likelihood function; Theoretically using the condition expected method infered the model parameters' posterior distribution, with which continued the study of the forecasting distribution; then make attempt to the inference of Bayesian MA(q) model; Also, through a series simulated by the SAS, implemented Bayesian MA(2) model simulation with WinBUGS.Further more, based on the analysis of Bayesian AR model and MA model , we analyzed the Bayesian ARMA(p,q) model and its mathematical structure. Mainly analyzed the Bayesian ARMA(1,1) model, and constructed the model condition likelihood function and the parameters' posterior distribution. Then through a series simulated by the SAS, we carried out the ARMA(1,1) model simulation analysis with WinBUGS.Finally, the Bayesian inference theory about VAR model under ther parameter's prior distributions is explored. Mainly studied the Baysian VAR(p) model under the"Non-information priors", which we reached the conclusion that its posterior distribution is in closed form. Examples with simulated and actual economic data are presented.