الفهرس 
Title: A comparison of approximate bayesian estimation methods for ARMA models
AbstractOnly 14 pages are availabe for public view
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Abstract
Autoregressive Moving Average (ARMA) models involve nonlinearity in the coefficients because of the unobserved lagged errors. This leads to complicated likelihood function and analytically intractable posterior density. Two approaches of approximation have been introduced in the literature to overcome the problem of posterior analysis. The first approach is the analytic approximations which includes four well known approximations: Newbold (N), Zellner and Reynolds (ZR), Broemeling and Shaarawy (BS) and Bayesian Generalized Least Squares (BGLS). The second approach is the approximation based on Markov Chain Monte Carlo (MCMC) which contains several methods, especially Gibbs sampling (G) and Metropolis Hastings (MH) algorithms. In previous studies the accuracy of MCMC methods have not been investigated in a wide scale as we do in this thesis. The convergence checking ofMCMCmethods in our study has been employed for 1000 data sets not for one sequence as usual. In addition, the convergence of MCMC methods has been checked at different sample sizes. Moreover, the analytic approximations and MCMC methods have not been compared. Accordingly, this study aims at comparing the accuracy of these two approaches for estimating ARMA models via extensive simulation studies along with real life example of time series. The simulation results show that the accuracy of all the approximation methods is improved as the sample size increases. The model order and the coefficient values do not affect the results. In addition, N and ZR approximations have the preference in estimating the model parameters, followed by BSNL and G. Moreover, MH and G always had a comparable MSE values in estimating the coefficients