This study approaches the Bayesian identification of moving average processes using an approximate likelihood function and a normal gamma prior density. The marginal posterior probability mass function of the model order is developed in a convenient form. Then one may investigate the posterior probabilities over the grid of the order and choose the order with the highest probability to solve the identification problem. A comprehensive simulation study is carried out to demonstrate the performance of the proposed procedure and check its adequacy in handling the identification problem. In addition, the proposed Bayesian procedure is compared with some non Bayesian automatic techniques and another Bayesian technique. The numerical results support the adequacy of using the proposed procedure in solving the identification problem of moving average processes.

The main objective of the current study is to handle the identification problem of autoregressive processes from the Bayesian point of view. Two Bayesian identification approaches are considered. They are referred to as the direct and the indirect approaches. The two approaches are employed to solve the Bayesian identification problem of autoregressive processes using three well known priors. These priors are the G prior, the Natural-Conjugate prior and Jeffrey's prior. The theoretical derivations related to the two Bayesian identification approaches are conducted using the above mentioned priors. Moreover, the performance of the two techniques, using each of the three priors, is investigated via comprehensive simulation studies. Simulation results show that the two techniques are adequate to solve the identification problem of autoregressive processes. The increase in the time series length leads to better performance for each technique. The use of different priors doesn't affect the numerical results.

The multivariate estimation problems arise if the observations are available for several related variables of interest. The multivariate time series may be found in many fields of application such as economics, meteorology and utilities. The current study has three main objectives. The first one is to develop an approximate convenient Bayesian methodology to estimate the parameters of multivariate moving average processes. The second objective is to investigate the numerical efficiency of the proposed technique in solving the estimation problems by conducting a wide simulation study. The last objective is to study the sensitivity of the numerical efficiency with respect to the parameters values and time series length. The results show that the proposed technique succeeded in estimating the parameters of the multivariate moving average processes. The results are not sensitive to the changes in parameter values or in time series length.

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