الفهرس 
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Abstract
This thesis proposes a new Bayesian approach for estimating autoregressive moving average (ARMA) models. This technique is based on replacing lagged errors of the original ARMA model with appropriately lagged residuals from a long autoregression. Unlike Bromeling and Shaarawy (1988), we assumed that the approximation error when replacing lagged innovations in the original ARMA model with lagged residuals from a long AR follows a white noise process. Then this white noise approximation error is used in deriving the posterior distribution of the ARMA model parameters. Moreover rather than assuming white noise, the exact structure of the approximation error when replacing true errors with corresponding residuals is derived and used in deriving the posterior distribution of the ARMA model parameters, then the second proposed estimator for ARMA model is presented. The estimators obtained are Bayesian version Generalized Least Squares estimators and hence are denoted by (BGLS). The proposed methods and Bromeling and Shaarawy’s method are compared using several simulation studies and a real data example. The proposed methods are used to estimate time series of Egyptian trading securities value.
In addition, the pure seasonal moving average (pure SMA) models are estimated using a white noise approximation error, then the Bayesian proposed method for estimating SMA models is compared with Shaarawy and Ismail’s method (1988) via several simulation studies.
Key words: GLS; approximation error; posterior distribution; Bayesian estimation; ARMA models; pure SMA models; series A ; Value of Egyptian trading securities